Problem 74
Question
Write each equation in its equivalent exponential form. Then solve for \(x .\) $$\log _{5}(x+4)=2$$
Step-by-Step Solution
Verified Answer
The value of \(x\) that satisfies the equation is \(x = 21\).
1Step 1: Convert to Exponential Form
By using the definition of logarithms, we can rewrite the given equation \(\log _{5}(x+4)=2\) in exponential form as \(5^2 = x+4\). This means that the base (5), raised to the power of the right side (2), is equal to the argument of the logarithm (\(x + 4\)).
2Step 2: Simplify the Equation
Calculate \(5^2\) to simplify the equation. This results in \(25 = x + 4\).
3Step 3: Solve for \(x\)
Finally, solve the equation \(25 = x + 4\) for \(x\). Subtract 4 from both sides of the equation to isolate \(x\), which gives \(x = 25 - 4 = 21\).
Other exercises in this chapter
Problem 73
Solve each logarithmic equation. Be sure to reject any value of \(x\) that is not in the domain of the original logarithmic expressions. Give the exact answer.
View solution Problem 73
Let \(\log _{b} 2=A\) and \(\log _{b} 3=C .\) Write each expression in terms of \(A\) and \(C\). $$\log _{b} \sqrt{\frac{2}{27}}$$
View solution Problem 74
Let \(\log _{b} 2=A\) and \(\log _{b} 3=C .\) Write each expression in terms of \(A\) and \(C\). $$\log _{b} \sqrt{\frac{3}{16}}$$
View solution Problem 75
Write each equation in its equivalent exponential form. Then solve for \(x .\) $$\log _{4} x=-3$$
View solution