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3/2 log4 -2/3 log8 + log2 = log x

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Answer:

I can help you solve this equation. First, let’s use the property of logarithms that says log_a(b) = log_c(b) / log_c(a) to convert all the logarithms to the same base. For convenience, let’s use base 2. We get:

3/2 log_2(4) - 2/3 log_2(8) + log_2(2) = log_2(x)

Next, let’s use the property of logarithms that says log_a(b^c) = c log_a(b) to simplify the logarithms of powers. We get:

3/2 * 2 log_2(2) - 2/3 * 3 log_2(2) + log_2(2) = log_2(x)

Next, let’s use the property of logarithms that says log_a(a) = 1 to simplify the logarithms of base 2. We get:

3 - 2 + 1 = log_2(x)

Next, let’s simplify the left side of the equation by adding and subtracting. We get:

2 = log_2(x)

Finally, let’s use the property of exponentiation that says a^log_a(b) = b to solve for x. We get:

x = 2^log_2(x) x = 2^2 x = 4

Therefore, the solution is x = 4. I hope this helps you understand how to solve this equation.

User Andre Zimpel
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