Problem 139 - Algebra and Trigonometry

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I can solve \(4^{x}=15\) by writing the equation in logarithmic form.

Step-by-Step Solution

Answer

The statement makes sense. The equation \(4^{x}=15\) can be converted into logarithmic form as \( \log_{4}{15}=x\) to make the solution process simpler.

Step 1: Understanding the statement

The statement says, 'I can solve \(4^{x}=15\) by writing the equation in logarithmic form.' This will be examined for the validity and reasoning behind it.

Step 2: Changing the equation to logarithmic form

The equation \(4^{x}=15\) can be converted to logarithmic form by applying the definition of logarithms. In this case, it will be written as \( \log_{4}{15}=x\). This means that 'x is the power to which 4 must be raised to get 15'.

Step 3: Evaluating the reasonability of the solution

Once the equation has been converted to logarithmic form, solving for x becomes more straightforward. This is because the x term that was previously in the exponent position is now isolated on one side of the equation, making it easier to solve. Therefore, the initial statement makes sense and it is indeed easier to solve the equation by converting it into logarithmic form.