Problem 16 - Introductory and Intermediate Algebra for College Students 4th

Question

Write each equation in its equivalent logarithmic form. $$15^{2}=x$$

Step-by-Step Solution

Answer

The equivalent logarithmic form of the given exponential equation \(15^{2} = x\) is \( \log_{15}(x) = 2\).

Step 1: Identify the structure of the given exponential expression.

The given expression is \(15^{2} = x\). In an exponential equation, the base is the number being multiplied, the exponent is the number of times the base number is being multiplied, and the result is the value obtained from the exponential expression.

Step 2: Apply the logarithmic conversion rule.

The conversion rule states that the exponent in a base 'b' to power 'p' equals 'a' equation can be written in logarithm form as \( \log_{b}(a) \). Applying this rule, our base 'b' is 15, our result 'a' is 'x', and the exponent 'p' is 2. Hence, \( \log_{15}(x) = 2\).

Step 3: Write the final logarithmic form.

The equivalent logarithmic form for the given exponential equation \(15^{2} = x\) is \( \log_{15}(x) = 2\).