Answer :
To solve the equation [tex]\(\log(x-3) = 2\)[/tex], we can use the properties of logarithms to find the value of [tex]\(x\)[/tex].
1. The equation [tex]\(\log(x-3) = 2\)[/tex] is in the base 10 logarithm (since no base is specified, we assume it's base 10). This means that the expression [tex]\(x-3\)[/tex] is equal to [tex]\(10^2\)[/tex].
2. Calculate [tex]\(10^2\)[/tex]:
[tex]\[
10^2 = 100
\][/tex]
3. Now, we know that [tex]\(x-3 = 100\)[/tex]. To solve for [tex]\(x\)[/tex], add 3 to both sides of the equation:
[tex]\[
x = 100 + 3
\][/tex]
4. This gives us:
[tex]\[
x = 103
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation is 103.
The answer is [tex]\( \boxed{103} \)[/tex].
1. The equation [tex]\(\log(x-3) = 2\)[/tex] is in the base 10 logarithm (since no base is specified, we assume it's base 10). This means that the expression [tex]\(x-3\)[/tex] is equal to [tex]\(10^2\)[/tex].
2. Calculate [tex]\(10^2\)[/tex]:
[tex]\[
10^2 = 100
\][/tex]
3. Now, we know that [tex]\(x-3 = 100\)[/tex]. To solve for [tex]\(x\)[/tex], add 3 to both sides of the equation:
[tex]\[
x = 100 + 3
\][/tex]
4. This gives us:
[tex]\[
x = 103
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation is 103.
The answer is [tex]\( \boxed{103} \)[/tex].
