How to change log to exponential form?
Understand the Problem
The question is asking how to convert a logarithmic expression into its equivalent exponential form. This involves rearranging the equation according to the properties of logarithms.
Answer
If $\log_b(x) = y$, then $b^y = x$.
Answer for screen readers
If $\log_b(x) = y$, then the equivalent exponential form is $b^y = x$.
Steps to Solve
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Identify the logarithmic expression First, identify the logarithmic expression you want to convert. For example, if you have the expression $\log_b(x) = y$, where $b$ is the base, $x$ is the number you're taking the log of, and $y$ is the result.
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Apply the definition of logarithms The definition states that if $\log_b(x) = y$, then you can rewrite this in exponential form as: $$ b^y = x $$
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Rearrange the equation Using the previous step, rearrange the logarithmic expression into its exponential form: For instance, if $\log_2(8) = 3$, it can be rewritten as: $$ 2^3 = 8 $$
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Validate the conversion Check if the rewritten exponential form is correct by calculating both sides. Ensure that the base raised to the exponent equals the original number.
If $\log_b(x) = y$, then the equivalent exponential form is $b^y = x$.
More Information
This conversion is based on the fundamental relationship between logarithms and exponents, which is critical in algebra and understanding functions.
Tips
- Incorrectly identifying the base or the argument of the logarithm.
- Forgetting to rearrange the equation correctly; ensure that the base, exponent, and result are correctly placed.
