Equation with Logarithm I want to solve the following

ideklaraz7xz

ideklaraz7xz

Answered question

2022-04-02

Equation with Logarithm
I want to solve the following equation:
3x3x1=243.
My approach is the following:
32x1=243 then
(2x1)log3=log243 and then:
x=log243log3+12
Is this correct?

Answer & Explanation

Charlie Haley

Charlie Haley

Beginner2022-04-03Added 14 answers

This is correct. Alternatively you could use the base 3 logarithm, in which case you obtain
x=12(log3243+1).
Now note that 243=35 so this reduces to x=12(5+1)=3
If instead you use your expression for x, then you have
x=12(log243log3+1)=12(log35log3+1)=12(5log3log3+1)=12(5+1)=3.
Yaritza Phillips

Yaritza Phillips

Beginner2022-04-04Added 12 answers

don't need to take log cause RHS also in same base .
32x1=243
32x1=352x1=5x=3
.By the way you were going on right track

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