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Chapter 26: Problem 751

Find the value of \(\mathrm{x}\) if \(\log _{4} 64=\mathrm{x}\).

Short Answer

Expert verified
Since \(4^3 = 64\), the value of x is \(x = 3\).

Step by step solution

01

Write the log equation in exponential form

To solve this logarithmic equation, we need to rewrite it in exponential form using the formula: \(log_{a}(b) = c \Rightarrow a^{c} = b\) In our case, \(a = 4\), \(b = 64\), and \(c = x\). So, we need to rewrite the equation as: \(4^{x} = 64\)
02

Find the value of x

To find the value of x, we'll use our knowledge of exponential numbers. We are looking for the value of x that makes the equation true: \(4^{x} = 64\) We know that \(4^1 = 4\), \(4^2 = 16\), and \(4^3 = 64\). Therefore, when \(x = 3\), the equation is true.
03

Write the final answer

We found the value of x that makes the equation true. So, the value of x is: \(x = 3\)

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