Question

solving logarithmic equations using the definition of a logar
solve the equation \\(\log_{4}(x + 20) = 3\\).
\\(x = \square\\)

Explanation:

Step1: Recall the definition of a logarithm

The logarithmic equation $\log_{b}(y) = x$ is equivalent to the exponential equation $b^{x}=y$. Here, $b = 4$, $x = 3$, and $y=x + 20$. So we can rewrite the logarithmic equation as an exponential equation: $4^{3}=x + 20$.

Step2: Calculate the value of $4^{3}$

We know that $4^{3}=4\times4\times4 = 64$. So the equation becomes $64=x + 20$.

Step3: Solve for $x$

Subtract 20 from both sides of the equation: $x=64 - 20$.
Calculating the right - hand side, we get $x = 44$.

Answer:

$x = 44$