Question

Which exponential equation is equivalent to this logarithmic equation?

log5 x - log5 25 = 7

A. 7^9=x
B. 5^9=x
C. 7^5=x
D. 5^5=x

Answer 1

`\displaystyle B)x = {5}^(9)`

Explanation:

we are given a logarithmic equation

`\displaystyle \log_(5)(x) - \log_(5)(25) = 7`

simplify the log:

`\displaystyle \log_(5)(x) -2 = 7`

add 2 to both sides:

`\displaystyle \log_(5)(x) = 9`

remember that,

`\displaystyle \log_(a)(b) = c \iff {a}^(c) = b`

so we obtain:

`\displaystyle x = {5}^(9)`

hence,

our answer is B)