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Question: Solve the following logarithmic equation: log4(64)=x \log_{4}(64) = x Enter your answer (opens in…

Solve the following logarithmic equation:

log4(64)=x \log_{4}(64) = x

Enter your answer (opens in new window)

x=0 x = \boxed{\phantom{0}}

Solution

To solve the logarithmic equation: log4(64)=x \log_4(64) = x First, rewrite the logarithmic equation in exponential form. This means: 4x=64 4^x = 64 Next, express 64 as a power of 4. Since 64=4364 = 4^3, we have: 4x=43 4^x = 4^3 Since the bases are the same, we equate the exponents: x=3 x = 3 Therefore, the solution is: x=3 x = 3

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