Question
Solve for x in the logarithmic equation 10log(105)=10x
10
log
(
10
5
)
=
10
𝑥
.(1 point)
x=
𝑥
=
10
log
(
10
5
)
=
10
𝑥
.(1 point)
x=
𝑥
=
Answers
GPT-4o mini
To solve the equation \( 10 \log(10^5) = 10x \), we can start simplifying the left side.
First, we know from the properties of logarithms that:
\[
\log(10^5) = 5
\]
because the logarithm of a base raised to a power is equal to that power.
Substituting this back into the equation gives us:
\[
10 \cdot 5 = 10x
\]
which simplifies to:
\[
50 = 10x
\]
Now, we can solve for \( x \) by dividing both sides by 10:
\[
x = \frac{50}{10} = 5
\]
So, the final answer is:
\[
\boxed{5}
\]
First, we know from the properties of logarithms that:
\[
\log(10^5) = 5
\]
because the logarithm of a base raised to a power is equal to that power.
Substituting this back into the equation gives us:
\[
10 \cdot 5 = 10x
\]
which simplifies to:
\[
50 = 10x
\]
Now, we can solve for \( x \) by dividing both sides by 10:
\[
x = \frac{50}{10} = 5
\]
So, the final answer is:
\[
\boxed{5}
\]