Solve logarithmic equations Give the exact answer Do not use

Solve logarithmic equations. Give the exact answer. Do not use a calculator. (Don\'t forget to consider the domain!) log) x^2 = log_3(6x + 7)

Solution

a). first step is we can remove log value since both side we have log same value

so we will get x^2 = (6x+7)

x^2 -6x -7 =0

x^2 -7x +x -7 =0

x(x-7) +1(x-7) =0

(x-7) (x+1) =0

so (x-7) = 0 or (x+1) =0

x = 7 or x =-1

both these values are in the domain , since we get positive values in log

so x = -1, 7