Simplify: log (1/1000) . Write as a single logarithm and simplify (DO NOT finddecimal approximations): 2 log 8 + log x -log 2. Expand and simplify (DO NOT findapproximations): ln(e/x). Solve for x: log 4 + log (x - 8) = 2

Gauge Roach

Gauge Roach

Answered question

2022-08-06

Simplify: log ( 1 / 1000 ) .
Write as a single logarithm and simplify (DO NOT finddecimal approximations):
2 log 8 + log x log 2.
Expand and simplify (DO NOT findapproximations): ln ( e / x ).
Solve for x: log 4 + log ( x 8 ) = 2

Answer & Explanation

Jaxson White

Jaxson White

Beginner2022-08-07Added 15 answers

a) log ( 1 / 1000 ) = log 1 log 1000 = log 1000 = 3
b) 2 log 8 + log x log 2 = log 8 2 + log x log 2 = log 64 + log x log 2 = log 64 x 2 = log 32 x
c) ln ( e / x ) = ln e ln x = 1 ln x
d) log 4 + log ( x 8 ) = 2
log ( 4 + ( x 8 ) ) = 2
log ( x 4 ) = 2
x 4 = 10 2 = 100
so x=100+4=104
babibell06cz

babibell06cz

Beginner2022-08-08Added 4 answers

Solution:
= 2 log ( 8 ) + log ( x ) log ( 2 )
Apply the power rule for logarithms.
= log ( 8 2 ) + log ( x ) log ( 2 )
Simplify.
= log ( 64 ) + log ( x ) log ( 2 )
Apply the multiplication rule of logarithms. (Since when you add two logs, you can multiply them together).
= log ( 64 x ) log ( 2 )
Apply the division rule of logarithms. (Since when you subtract two logs, you can divide them together).
= log ( 64 x 2 )
Simplify.
= log ( 32 x )

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?