Solve for x in the logarithmic equation 10log(105)=10x

Question

10
log
⁡
(
10
5
)
=
10
𝑥
.(1 point)
x=
𝑥
=

Answer 1

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:

\[ \boxed{5} \]