Question
Solve the following logarithmic equation. Remember to check your solution log (x+4) =2
Answers
GPT-4o mini
To solve the logarithmic equation given by
\[
\log(x + 4) = 2,
\]
we first convert the logarithmic equation to its exponential form. The base of the logarithm is 10 (since it's not specified, we assume it's base 10). Therefore, we can rewrite the equation as:
\[
x + 4 = 10^2.
\]
Calculating \(10^2\) gives us:
\[
x + 4 = 100.
\]
Next, we solve for \(x\) by subtracting 4 from both sides:
\[
x = 100 - 4,
\]
\[
x = 96.
\]
Now, we need to check the solution to ensure that it does not produce any invalid logarithmic input. The argument of the logarithm must be greater than zero:
\[
x + 4 > 0.
\]
Substituting \(x = 96\) into this inequality:
\[
96 + 4 > 0,
\]
\[
100 > 0.
\]
This is true, so our solution is valid.
The solution to the equation \( \log(x + 4) = 2 \) is
\[
\boxed{96}.
\]
\[
\log(x + 4) = 2,
\]
we first convert the logarithmic equation to its exponential form. The base of the logarithm is 10 (since it's not specified, we assume it's base 10). Therefore, we can rewrite the equation as:
\[
x + 4 = 10^2.
\]
Calculating \(10^2\) gives us:
\[
x + 4 = 100.
\]
Next, we solve for \(x\) by subtracting 4 from both sides:
\[
x = 100 - 4,
\]
\[
x = 96.
\]
Now, we need to check the solution to ensure that it does not produce any invalid logarithmic input. The argument of the logarithm must be greater than zero:
\[
x + 4 > 0.
\]
Substituting \(x = 96\) into this inequality:
\[
96 + 4 > 0,
\]
\[
100 > 0.
\]
This is true, so our solution is valid.
The solution to the equation \( \log(x + 4) = 2 \) is
\[
\boxed{96}.
\]