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Question Video: Converting an Equation from Logarithmic to Exponential Form Mathematics • 10th Grade

Consider the logarithmic equation log₅ 25 = 𝑥. Convert the equation to exponential form. Solve the equation.

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Video Transcript

Consider the logarithmic equation log base five of 25 is equal to 𝑥. Convert the equation to exponential form. Solve the equation.

In order to convert from logarithmic form to exponential form, we recall that if log base 𝑎 of 𝑥 is equal to 𝑏, then 𝑥 is equal to 𝑎 to the power of 𝑏. In this question, the base 𝑎 is equal to five. The variable 𝑏 in the general rule is equal to 𝑥. Finally, the value for 𝑥 in the general rule is now 25. This means that 25 is equal to five to the power of 𝑥. We can use this rule to convert from logarithmic form to exponential form or vice versa.

In order to solve the equation, we recall that five squared is equal to 25, as five multiplied by five is 25. The solution to the equation five to the power of 𝑥 equals 25 is 𝑥 equals two.

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