how to solve this equation?

Question

Solve the equation: 7^(x+1)=4^2x. Round answer to 2 decimal places

Answer 1

The first step would be to take the logarithm of both sides and get, (x+1)log(7)=(2x)log(4). Then you would distribute the log(7) on the left to get, (x)log(7)+log(7)=(2x)log(4).

From here you gather your x terms to the right side of the equation and get,

log(7)=(2x)log(4)-(x)log(7).

The we factor out the x on the right side of the equation to get.

log(7)=x[2log(4)-log(7)].

Then divide and you get your value for x.