log3 x = log3 2 + log3 8 - log3 4 What is x

To solve the equation log3 x = log3 2 + log3 8 - log3 4, you can use the properties of logarithms.

Step 1: Combine the right side of the equation using the properties of logarithms. The sum of two logarithms with the same base can be written as a single logarithm by multiplying the arguments (log_b(m) + log_b(n) = log_b(mn)). The difference of two logarithms with the same base can be written as a single logarithm by dividing the arguments (log_b(m) - log_b(n) = log_b(m/n)).

So, log3 2 + log3 8 - log3 4 = log3 (2*8/4) = log3 4.

Step 2: Now, the equation is log3 x = log3 4.

Step 3: If log_b(m) = log_b(n), then m = n. So, x = 4.