Solve the given logarithmic equation 3 log x 125 The solutio

Solve the given logarithmic equation -3 log x 125 The solution set is {L} (Simplify your answer.)

Solution

1) logx(1/125) = 3

use the log property: log_ab = y ----> b = a^y

logx(1/125) = 3

(1/125) = x^3

x = (1/25)^1/3 = 1/5

x= 1/5

2) log_m(sqrt(5r^7/z^3)

Use the log properties:

log(A*B/C) = logA + logB -logC

and logA^r = r*logA

So, log_m(sqrt(5r^7/z^3)

= log_m(5r^7)^1/2 - log_mz^3/2

= (1/2)log_m(5r^7) - 3/2log_mz

=(1/2)log_m5 + 7/2log_mr - 3/2log_mz

=(1/2) { log_m5 + 7log_mr + 3log_m(1/z) }

= (1/2) { log_m5 + 7log_mr + log_m(1/z^3) }

Option A