Questions: Evaluate the expression without using a calculator. log4 4^3 log4 4^3=

Transcript text: Evaluate the expression without using a calculatio. \[ \log _{4} 4^{3} \] \[ \log _{4} 4^{3}= \] $\square$

Solution

Solution Steps

To evaluate the expression $\log_{4} 4^{3}$, we can use the property of logarithms that states $\log_{b} b^{x} = x$. Here, the base $b$ is 4 and the exponent $x$ is 3. Therefore, $\log_{4} 4^{3} = 3$.

Step 1: Identify the Expression

We need to evaluate the expression $ \log_{4} 4^{3} $.

Step 2: Apply Logarithmic Properties

Using the property of logarithms, we know that $ \log_{b} b^{x} = x $. In this case, we have: \[ \log_{4} 4^{3} = 3 \]

Final Answer

Thus, the final answer is $ \boxed{3} $.

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