5 Write the expression as the sum or difference of two logar

5. Write the expression as the sum or difference of two logarithmic functions containing no exponents.

Solution

log₅x cube root(x+8)

We have to use some log rules here and the first rule which we have to use is

log_axy=log_ax+log_ay

Therefore log₅x cuberoot(x+8) = log₅x+log_x(x+8)^1/3

The second log rule we have to use is

log_ax^b = b log_ax

log₅x+log₅(x+8)^1/3= log₅x + (1/3)log₅(x+8)