Solve the equation for x by using base 10 logarithms. 16*4^(2.5x)=70

Marcus Bass 2022-09-17 Answered
solve the equation using logarithms (I think this is easy level)
Solve the equation for x by using base 10 logarithms.
16 4 2.5 x = 9
EDIT: I made a typo (somehow... I was very far off!!)
The correct equation is this:
16 4 2.5 x = 70
Can it be written like:
2.5 x log 10 ( 5 ) = 70   ?
Then get:
log 10 ( 5 ) = 70 2.5 x
The computer wants a largest value and smallest value, similar to an answer for a quadratic problem. I need to know how to get the 2 answers even if one ends up negative (I know the negative will be tossed out, but I still need to know how to get the answer).
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (2)

Matthias Calhoun
Answered 2022-09-18 Author has 4 answers
16 4 2.5 x = 70 2 4 ( 2 2 ) 2.5 x = 70 2 4 2 5 x = 70 2 4 + 5 x = 70 log 10 2 4 + 5 x = log 10 70 ( 4 + 5 x ) log 10 2 = log 10 70 4 + 5 x = log 10 70 log 10 2
Can you take it from here?
Addendum :
4 2 ( 2 2 ) 2.5 x = 70 4 2 ( 2 2 ) 2.5 x ( 70 ) 2 = 0 ( 4 2 2.5 x 70 ) ( 4 2 2.5 x + 70 ) = 0
It will yield two solutions like you want.
Not exactly what you’re looking for?
Ask My Question
Harrison Mills
Answered 2022-09-19 Author has 2 answers
16 4 2.5 x = 16 ( 4 2.5 ) x = 16 ( 4 5 2 ) x = 16 32 x
So, 32 x = 9 16
Thus, x = log 32 ( 9 16 ) = log 10 ( 9 16 ) log 10 ( 32 )
For the updated equation
16 4 2.5 x = 16 ( 4 2.5 ) x = 16 ( 4 5 2 ) x = 16 32 x
So, 32 x = 30 16
Thus, x = log 32 ( 30 16 ) = log 10 ( 15 8 ) log 10 ( 32 )
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-04-09
Use identities to simplify log(a2+b2)2
Use logarithmic identities to simply the following:
log(a2+b2)2
I started with
log(a2+b2)2=2log(a2+b2)
I think it's not the final result, but I don't know how to proceed. Any hints would be helpful.
asked 2022-06-24
How to prove if log is rational/irrational
I'm an English major, now doubling in computer science. The first course I'm taking is Discrete Mathematics for Computer Science, using the MIT 6.042 textbook.
Within the first chapter of the book's practice problems, they ask us multiple times to prove that some log function is either rational or irrational.
Specific cases make more sense than others, but I would really appreciate any advice on how to approach these problems. Not how to carry them out algebraically, but what thought constructs are necessary to consider a log being (ir)rational.
For example, in the case of 2 2 log 2 3 , proving that 2 log 2 3 is irrational (and therefore a b , when a = 2 and b = 2 log 2 3 is rational) is not an easily solvable problem. I understand the methods of proofs, but the rules of logs are not intuitive to me.
A section from my TF's solution is not something I would know myself to construct:
Since 2 < 3 we know that log 2 3 is positive (specifically it is greater than 1), and hence so is 2 log 2 3. Therefore, we can assume that a and b are two positive integers. Now 2 log 2 3 = a / b implies 2 2 log 2 3 = 2 a / b . Thus
2 a / b = 2 2 log 2 3 = 2 log 2 3 2 = 3 2 = 9 ,
and hence 2 a = 9 b
Any advice on approaching thought construct to logs would be greatly appreciated!
asked 2022-07-01
Maclaurin series of ln ( 2 + x 2 )
I know that ln ( 1 + x ) = n = 1 ( 1 ) n 1 n x n
So is ln ( 1 + x 2 ) = n = 1 ( 1 ) n 1 n x 2 n ?
I don't know what to do next then.
asked 2022-08-08
What are logarithms?
I have heard of logarithms, and done very little research at all. From that little bit of research I found out its in algebra 2. Sadly to say, I'm going into 9th grade, but yet I'm learning [calculus!?] and I don't know what a logarithm is! I find it in many places now. I deem it important to know what a logarithm is even though I'm jumping the gun in a sense. My understanding of concepts, is just like that of programming. In the mean time, you know its there, and your ITCHING SO HARD to find out what that is, but nope! For now we use it, tomorrow we learn what it does.
I just know that to identify a logarithm at my level, I just look for a log. :P
asked 2022-09-05
The mass m (t) remaining after t days from a 40 gram sample of thourium-234 is given by m ( t ) = 40 e 0.0277 t . What is the half-life of thorium-234?
asked 2022-08-28
How to generate log function that intersects at ( 0 , 1 ) and ( 1 , 0 )?
I apologize for any incorrect or missing formatting, first time posting in the math stack exchange. It's been a few years since I've done any kind of calculus, so I remember nothing at all, which is probably the reason why I find my self stumped so early in my calculations.
I'm looking to generate a logarithmic algorithm that will follow a plot that will pass the following points: ( 0 , 1 ) and ( 1 , 0 ). My end goal is to generate a programming function that will return a very simple repulsion force ceofficient value based on a distance between two points. I would like, however, that the force drop (logarithmic?) the further these two points are, and grow (exponentially?) the closer they get. This is in no way an accurate calculation I'm looking for, but merely a non-linear function to return me a scalar coefficient between 0 and 1 that I can manipulate later on.
I want the function to cross at ( 1 , 0 ) and ( 0 , 1 ) so I get a coefficient between 0 and 1. In my function, any Y value lower than 0 will be floored at 0 and likewise for Y values over 1 (where x < 0, which is possible since my X value in my algorithm will likely be an offsetted value of the distance between two points).
That being said, with the following few assumptions:
1. y = 0 when x = 1
2. y = 1 when x = 0
3. y < 0 when x > 1
4. y > 1 when x < 0
5. y = A l o g ( x + B ) + C
6.assuming log is log based 10
I tried to deduce the A , B , C constants in order to generate a formula.
Here is what I've done so far:
1.From assumption #1, I can generate 1 = A l o g ( B ) + C
2.From assumption #2, I can generate 0 = A l o g ( 1 + B ) + C
3.I make both equations equals by transforming equation from 1. to 0 = A l o g ( B ) + C 1
4.Making the following equality: A l o g ( B ) + C 1 = A l o g ( 1 + B ) + C
5.I can scratch both C constants out (is it safe to assume C = 0, or C can be equal to any arbitrary value, without changing the equation's plot?): A l o g ( B ) 1 = A l o g ( 1 + B )
6.Dividing each part by A gets me: A l o g ( B ) A 1 A = A l o g ( 1 + B ) A
7.Allowing me to reduce both logs: log ( B ) 1 A = l o g ( 1 + B )
8.If I put both logs on the same side: l o g ( B ) l o g ( 1 + B ) = 1 A
9.I can combine them into: log ( B 1 + B ) = 1 A
And I'd say this is where I'm stuck; I have two unknowns ( A and B) with one equation to solve. I don't know where to go from here. What's the next step?
asked 2021-12-05
Write log(x)=y in exponential form.