An interesting log problem 3^((log_3(x))^2)+x^(log_3x)=162 How do I go about doing this.

Layla Fisher

Layla Fisher

Answered question

2022-11-23

An interesting log problem 3 ( l o g 3 x ) 2 + x l o g 3 x = 162
How do I go about doing this. I am stuck at the step x log 3 x = 81. Is this right? How do I continue or is it wrong?

Answer & Explanation

driwant9HB

driwant9HB

Beginner2022-11-24Added 11 answers

This is correct, next step is to take the 3-log of both sides:
log 3 ( x log 3 x ) = ( log 3 x ) ( log 3 x ) = log 3 81 = 4
So log 3 x = ± 2 which means that x = 3 2 = 9 or x = 3 2 = 1 / 9
As for the first step that is correct log 3 3 ( log 3 x ) 2 = ( log 3 x ) 2 log 3 3 = ( log 3 x ) 2 = log 3 ( x log 3 x ), so the terms on the left hand side are equal.
This means that the first step is complicating things as you could drop the second term instead and get
3 ( log 3 x ) 2 = 81
which seems to lead to a more straight forward solution (but that's only up to a matter of opinion).

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?