Question

What is x equal to in the equation log(10^5⋅10^x)=12

Answer 1

To solve the equation \( \log(10^5 \cdot 10^x) = 12 \), we can start by simplifying the left-hand side.

Using the properties of logarithms, specifically that \( \log(a \cdot b) = \log a + \log b \), we can rewrite the equation:

\[
\log(10^5 \cdot 10^x) = \log(10^5) + \log(10^x)
\]

Now, we can apply the logarithm power rule, which states \( \log(10^a) = a \), to each term:

\[
\log(10^5) = 5
\]
\[
\log(10^x) = x
\]

Therefore, we can rewrite the original equation as:

\[
5 + x = 12
\]

Now, we solve for \( x \):

\[
x = 12 - 5
\]
\[
x = 7
\]

Thus, the value of \( x \) is \( \boxed{7} \).