Simple Logarithmic question. I was just wondering if i can do this. Q. Solve log_9 24=x =>9^x=24 => 3^(2x)=2^3 3 =>log_3(3^(2x))=log_3(2^3 3)

faois3nh

faois3nh

Answered question

2022-10-11

Simple Logarithmic question.
I was just wondering if i can do this.
Q. Solve log 9 24 = x
9 x = 24
3 2 x = 2 3 3
log 3 ( 3 2 x ) = log 3 ( 2 3 3 )
2 x = 2 ( 3 ) 1 / 3
x = 3 1 / 3
Is this actually correct or did i break some kind of log rule here? My answer appears to be out by 0.0038 compared to the book is that cause they used a calculator or is it just a fluke that my answer is so close?

Answer & Explanation

Amadek6

Amadek6

Beginner2022-10-12Added 21 answers

Your method is incorrect as pointed out by Mufasa (sorry I didn't spot that earlier) but it's not the way I'd have done it anyway (and probably not how the book answer was obtained). This way is better:
9 x = 24
x ln 9 = ln 24
x = ln 24 ln 9 = 1.44639...

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