To solve the equation $\log(x+5) = 2$, we proceed as follows:

Step 1: Understand the logarithmic equation

The logarithmic equation $\log(x+5) = 2$ is understood to be in base 10 (common logarithm). By the definition of logarithms:

$\log_b(a) = c \implies a = b^c$

Here, $b = 10$, $a = x+5$, and $c = 2$.

Step 2: Rewrite the equation

Using the definition of logarithms:

$x + 5 = 10^2$

Step 3: Simplify the equation

$x + 5 = 100$

Step 4: Solve for $x$

Subtract 5 from both sides:

$x = 100 - 5 = 95$

Final Answer:

$x = 95$

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Related Questions:

1. What are the properties of logarithms, and how do they apply in solving equations?
2. How would the solution differ if the base of the logarithm were not