How do you solve

6log2x = 13

I got

log2x^5 = 13

but I don't know what to do next.

Would it be 2x^5 = 13^2

HELP. Thanks.

6log2x=13

log2x=13/6
2x=10^13/6

x=73.39

thanks Dr. Russ!

To solve the equation 6log2x = 13, you were correct in applying the property of logarithms to rewrite it as log2x^5 = 13. However, your next step needs a slight adjustment.

To isolate x in log2x^5 = 13, you should get rid of the logarithm by applying the exponential function to both sides of the equation.

Here's the correct step-by-step process:

1. Start with the equation: log2x^5 = 13.
2. Rewrite the equation in exponential form: 2^(log2x^5) = 2^13.
3. Since the logarithm and exponential functions are inverse operations, applying 2 as the base to both sides of the equation cancels out the logarithm.
Resulting in: x^5 = 2^13.
4. Simplify the right side of the equation: x^5 = 8192.
5. To solve for x, you need to take the fifth root of both sides to undo the exponentiation.
Resulting in: (x^5)^(1/5) = 8192^(1/5).
6. Simplify the left side of the equation: x = 2.
7. Simplify the right side of the equation: x = 2.

Therefore, the solution to the equation 6log2x = 13 is x = 2.

Remember to always verify your answer by substituting it back into the original equation to confirm its validity.