Find the exact value. log 81 √(3) A) 1 4 B) 1 8 C) 1 12 D) 1 16

Question

Find the exact value.

log 81
`√(3)`
A)
1
4
B)
1
8
C)
1
12
D)
1
16

Answer 1

1/8

Explanation:

log 81 sqrt(3)

log 81 (sqrt(3)) =x

Rewriting as an exponential expression

81 ^x =sqrt(3)

We know that 81 = 3^4

3^4^x = 3^1/2

We know a^b^c = a^ (bc)

3 ^(4x) = 3^1/2

The bases are the same so the exponents are the same

4x =1/2

Divide each side by 4

4x/4 = 1/2/4

x =1/8