Multiple Choice
Convert the following logarithmic expression to its equivalent exponential form.
0. Functions
Logarithmic Functions
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Convert the following logarithmic expression to its equivalent exponential form.
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Verified step by step guidance1
Step 1: Recall the relationship between logarithmic and exponential forms. The general rule is: if \( \log_b(a) = c \), then \( b^c = a \).
Step 2: Identify the base, the result, and the exponent in the given logarithmic expression \( \log_4(x) = 5 \). Here, the base is \( 4 \), the result is \( x \), and the exponent is \( 5 \).
Step 3: Rewrite the logarithmic expression \( \log_4(x) = 5 \) in its equivalent exponential form using the rule from Step 1. This gives \( 4^5 = x \).
Step 4: Simplify the exponential expression if needed. In this case, \( 4^5 \) can be calculated, but the problem does not require the final numerical value.
Step 5: Conclude that the equivalent exponential form of the given logarithmic expression is \( 4^5 = x \).
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