Find the exact value of each logarithm without using a calculator.

$\mathrm{ln}e}^{3$

aortiH
2021-11-09
Answered

Find the exact value of each logarithm without using a calculator.

$\mathrm{ln}e}^{3$

You can still ask an expert for help

Sally Cresswell

Answered 2021-11-10
Author has **91** answers

Step 1

We have to find the exact value of the logarithmic expression:

$\mathrm{ln}e}^{3$

We know the properties of logarithms,

$\mathrm{ln}\left({a}^{m}\right)=m\mathrm{ln}\left(a\right)$

$\mathrm{ln}\left(a\right)={\mathrm{log}}_{3}\left(a\right)$

${\mathrm{log}}_{a}\left(a\right)=1$

$\mathrm{ln}\left(e\right)=1$

Step 2

Applying above properties for the given expression, we get

$\mathrm{ln}\left({e}^{3}\right)=3\mathrm{ln}\left(e\right)$

$=3\times 1$

$=3$

Hence, exact value of the expression is 3.

We have to find the exact value of the logarithmic expression:

We know the properties of logarithms,

Step 2

Applying above properties for the given expression, we get

Hence, exact value of the expression is 3.

asked 2022-01-21

Why are the domains for $\mathrm{ln}x}^{2$ and $2\mathrm{ln}x$ different?

asked 2021-11-07

Solve the exponential equation ${e}^{4x-5}-7=11243$ . Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.

asked 2022-04-05

Doubt on Logarithms multiplication

today I'm in doubt on calculating the follow expression${\mathrm{log}}_{4}3\cdot {\mathrm{log}}_{9}32$

Changing all to base 4: Working on:$\mathrm{log}}_{4}3\cdot \frac{{\mathrm{log}}_{4}32}{{\mathrm{log}}_{4}9$

Ending with:$\mathrm{log}}_{4}3\cdot \frac{2+{\mathrm{log}}_{4}2}{2\cdot {\mathrm{log}}_{4}3$

There's a way to simplify it more ? Also, do you know any resource explaining more on rules on every kind of operation with logs ?

Thanks in advance

today I'm in doubt on calculating the follow expression

Changing all to base 4: Working on:

Ending with:

There's a way to simplify it more ? Also, do you know any resource explaining more on rules on every kind of operation with logs ?

Thanks in advance

asked 2022-03-12

What is wrong with this solution?

$\mathrm{ln}\left(x\right)=1+\mathrm{ln}\left(5\right)$

$x={e}^{1+\mathrm{ln}\left(5\right)}={e}^{1+5}={e}^{6}$

What exactly am I doing wrong here?

What exactly am I doing wrong here?

asked 2021-11-06

Describe the power rule for logarithms and give an example.

asked 2021-01-15

Solve the equation and find the exact solution:

$\mathrm{log}base2\left(\mathrm{log}base3\left(\mathrm{log}base4\left(x\right)\right)\right)=0$

asked 2021-11-08

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.

$\mathrm{log}}_{424}-{\mathrm{log}}_{46$

A. 4

B. 24

C. 1

D. 6

A. 4

B. 24

C. 1

D. 6