Question

What is the exact value of the exponential equation, 5(10)4x=75 ?

c. x=log15/4
d. x=log70/4

Answer 1

c

Explanation:

using the law of logarithms

log
`x^(n)` ⇔ nlogx

given 5(
`(10)^(4x)` = 75 ( divide both sides by 5 )

`(10)^(4x)` = 15 ( take log of both sides )

log
`10^(4x)` = log15

4xlog10 = log15 ← log10 = 1

4x = log15 ( divide both sides by 4 )

x =
`(log15)/(4)` → c