Textbook Question
Convert the following expressions to the indicated base.
using base e
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
Identify the given logarithmic expression: \( x = \log_{9}(10) \). This means that 9 raised to the power of x equals 10.
Recall the definition of a logarithm: \( \log_{b}(a) = c \) implies \( b^{c} = a \). In this case, \( b = 9 \), \( a = 10 \), and \( c = x \).
Convert the logarithmic expression to its exponential form using the definition: \( 9^{x} = 10 \).
Verify the conversion by checking that the base raised to the power of the logarithm equals the original number: \( 9^{x} = 10 \) confirms the conversion.
Understand that the exponential form \( 9^{x} = 10 \) is equivalent to the original logarithmic expression \( x = \log_{9}(10) \).
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