Multiple Choice
Convert the following exponential expression to its equivalent logarithmic 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 \( y = \log_b(x) \), then it can be rewritten as \( b^y = x \).
Step 2: Identify the base, the exponent, and the result in the given logarithmic expression. Here, the base is \( 9 \), the exponent is \( x \), and the result is \( 10 \).
Step 3: Rewrite the logarithmic expression \( x = \log_9(10) \) in its equivalent exponential form using the rule from Step 1. This becomes \( 9^x = 10 \).
Step 4: Verify that the rewritten exponential form \( 9^x = 10 \) is consistent with the original logarithmic expression \( x = \log_9(10) \).
Step 5: Conclude that the equivalent exponential form of the given logarithmic expression is \( 9^x = 10 \).
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