Write the expression as a single logarithm 7 logm x 13 logm

Write the expression as a single logarithm. 7 log_m x - 1/3 log_m w + 6 log_m z

Solution

we know that:

log m + log n = log mn

log m - log n = log (m/n)

log m^n = n*log m

Now given equation is

7*log_mx - (1/3)*log_mw + 6*log_mz

= log_mx⁷ - log_mw^1/3 + log_mz⁶

= log_m(x⁷*z⁶/w^1/3)