What value will satisfy this equation: 18^(4x-3)=(54sqrt(2))^(3x-4) Please use the logarithm method. I am having a problem in expressing 54sqrt(2) in the power of 18. My book simply says that it is 18^(3/2). But I can't understand how.

detineerlf

detineerlf

Answered question

2022-07-17

How to use the logarithm method to solve 18 4 x 3 = ( 54 2 ) 3 x 4 for x?
What value will satisfy this equation:
Please use the logarithm method. I am having a problem in expressing 54 2 in the power of 18. My book simply says that it is 18 3 / 2 . But I can't understand how.

Answer & Explanation

dtal50

dtal50

Beginner2022-07-18Added 10 answers

54 2 = 18 3 2 = 18 1 8 = 18 3 2 as the square root is also the positive one half exponent which can added if the terms of multiplied.
Thus, your problem could be rewritten as 4 x 3 = 3 ( 3 x 4 ) 2 which could be rewritten as 8 x 6 = 9 x 12 which is fairly easy to solve.
Libby Owens

Libby Owens

Beginner2022-07-19Added 3 answers

Hint: First,
18 3 / 2 = 18 18 = 18 3 2 (1) = 54 2
Therefore, log ( 54 2 ) = 3 2 log ( 18 )
Next, take the log of both sides of your equation and use ( 1 )

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