Solve log_5(x) = 2
Logarithmic equation, worked out line by line the way a teacher would write it.
Answer
| Solution | x = 25 |
Step-by-step solution
4 steps-
1 Given\log_{5}{\left(x \right)} = 2
Solve for x.
-
2 Domain: the argument of every logarithm must be positive
A logarithm is defined only for positive numbers, so every log argument must be greater than 0. Any answer that breaks this is rejected at the end.
x > 0 -
3 Rewrite in exponential form: log_5(g) = d means g = 5^d
A logarithm answers the question “which power gives this number?”: log_b(g) = d means b^d = g. Rewriting it that way removes the logarithm.
x = 5^{2} = 25 -
4 Check\begin{aligned}x = 25:\quad 2 = 2\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 25 | 2 | 2 | ✓ |
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