6. Exponential and Logarithmic Functions

Introduction to Logarithms

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Multiple Choice

Change the following logarithmic expression to its equivalent exponential form.
$\log_4x=5$

$4^{x}=5$

$x^4=5$

$4^5=x$

$5^4=x$

Verified step by step guidance

Identify the given logarithmic equation: $ \log_4{x} = 5 $.

Recall the definition of a logarithm: $ \log_b{a} = c $ means $ b^c = a $.

Apply the definition to the given equation: $ \log_4{x} = 5 $ implies $ 4^5 = x $.

Rewrite the equation in exponential form: $ x = 4^5 $.

The equivalent exponential form of the logarithmic expression is $ x = 4^5 $.

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Change the following logarithmic expression to its equivalent exponential form.log4x=5\log_4x=5log4x=5