Solve the following equation analytically Enter your answers

Solve the following equation analytically. (Enter your answers as a comma-separated list.) log7(x4) = log7(x)

Solution

log7(x4) = log7(x)

Use log properties: logx(A) = logx(B) ---> A = B

So, x^4 = x

x( x^3 -1) =0

x = 0 ;

for logx function x>0

x ^3 -1 =0 ---> (x -1)(x^2 +x +1) =0

x^2 +x +1 =0

gives complex solution

So, solution of x is x =1