Write the expression as a single logarithm 4 loga6x7 loga8x

Write the expression as a single logarithm. 4 log_a(6x^7) - log_a(8x + 15) 4 log_a(6x^7) - 1/3 log_a (8x + 15) = (Simplify your answer.)

Solution

4loga(6x^7) -(1/3)loga(8x +15)

use the following log properties:

logx^a = a*logx ; logA -logB = log(A/B)

4loga(6x^7) -(1/3)loga(8x +15) = loga(6x^7)^4 - loga(8x + 15)^1/3

= loga(1296x^28/(8x+5)^1/3 )