Logarithmic Equation: Solve for x log_(3x)81=2

Janiah Parks

Janiah Parks

Answered question

2022-10-10

Logarithmic Equation: Solve for x
log 3 x 81 = 2
How would I go about solving this? This is what I tried:
log 3 x 81 = 2
log 81 log 3 + log x = 2
Where do I go from here?
If I isolate log x on one side, how do I get rid of the log?

Answer & Explanation

Jaylyn George

Jaylyn George

Beginner2022-10-11Added 6 answers

log 3 x ( 81 ) = 2 is equivalent to
( 3 x ) 2 = 9 x 2 = 81
by the definition of the logarithm.
9 x 2 = 81 x 2 = 9
This gives solutions x = 3 and x = 3, but only x = 3 is a solution, since the base of a logarithm must be greater than zero.
emmostatwf

emmostatwf

Beginner2022-10-12Added 2 answers

For any two real numbers b and x where b is positive and b 1,
y = b z z = log b ( y )
so for log 3 x 81 = 2 we have
( 3 x ) 2 = 81 = ( 3 3 ) 2 x = 3

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?