How do you simplify the following expression? log(3^(5^7)) I know that logarithms are like the inverse of exponents, but are there any tricks to simplify powers inside logarithms? Edit: There are five answer choices: (A) 7log(3^5) (B) 35log(3) (C) 7(log(3))(log(5)) (D) 7(log(3)+log(5)) (E) 5^7log(3)

Josie Kennedy

Josie Kennedy

Answered question

2022-11-14

Properties of Logarithms
How do you simplify the following expression?
log ( 3 ( 5 7 ) )
I know that logarithms are like the inverse of exponents, but are there any tricks to simplify powers inside logarithms?
Edit: There are five answer choices:
(A) 7 log ( 3 5 )
(B) 35 log ( 3 )
(C) 7 ( log ( 3 ) ) ( log ( 5 ) )
(D) 7 ( log ( 3 ) + log ( 5 ) )
(E) 5 7 log ( 3 )

Answer & Explanation

Faith Wise

Faith Wise

Beginner2022-11-15Added 17 answers

As log ( a m ) = m log a where both log remain defined
Here a = 3 , m = 5 7
Zackary Diaz

Zackary Diaz

Beginner2022-11-16Added 4 answers

log 3 ( 5 7 ) = 5 7 log 3The power on the inside become multiplication on the outside, and becomes the simplest form (unless you want to turn 5 7 into a single long number instead of that power)

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