The first step in solving this log equation is to use the power rule for logarithms to expand the left side of the equation. This will give you two separate log terms.
To combine the two log terms, you can use the product rule for logarithms. This rule states that log(a*b) = log(a) + log(b). In this case, you will have log(2^x) + log(4^(x+5)).
You can use the properties of logarithms to simplify the log terms. In this case, you can use the power rule for logarithms to bring the exponents in front of the logs. This will give you x*log(2) + (x+5)*log(4).
Once the log terms are simplified, you can use algebraic methods to solve for x. In this case, you can use the distributive property to factor out x, leaving you with x*(log(2) + log(4)) + 5*log(4) = 4^(2x-1).
This log equation could have one or two solutions. To determine the number of solutions, you will need to solve the equation and then check if your solutions are valid. If your solutions result in negative numbers or zero inside the logarithms, they are not valid solutions. If your solutions are valid, then there will be two solutions. If one of your solutions is not valid, then there will be one solution.