Question

Solve for x in the logarithmic equation 10log(1024)=10x
10
log
⁡
(
10
24
)
=
10
𝑥
.(1 point)
Responses

x=10
𝑥
=
10
x is equal to 10

x=2410
𝑥
=
24
10
x is equal to 24 to the 10th power

x=1024
𝑥
=
10
24
x is equal to 10 to the 24th power

x=24

Answer 1

To solve the equation \( 10\log(1024) = 10x \), we can simplify it.

1. First, we can divide both sides by 10:

\[
\log(1024) = x
\]

2. Next, we can evaluate \( \log(1024) \). We know that:

\[
1024 = 2^{10}
\]

Thus, using the change of base and logarithmic properties:

\[
\log(1024) = \log(2^{10}) = 10\log(2)
\]

However, we generally focus on \( \log_{10} \) unless specified otherwise, so we can keep it as \( \log(1024) \).

For base 10 logs,

\[
\log_{10}(1024) \approx 3.0103
\]

This doesn't give us an exact integer.

To find \( 10x \), since we simplified to \( x = \log(1024) \), to get the options you provided:

Given the choices:

- \( x = 10 \)
- \( x = 24 \times 10 \)
- \( x = 10^{24} \)
- \( x = 24 \)

The correct choice is:

\[
x \approx 10 \log(2)
\]

Since none of the options match \( x \approx 3.0103 \), it's likely that the problem expects an understanding or approximation rather than an exact fit.

However, looking at your original formulation \( \log(1024) = 10x \), the most logical option based on \( x \) and \( \log(1024) \approx 3.0103 \) would lead us to assuming \( x = 10 \).

Thus, the correct answer from the options present is:

**x = 24** (since \( 10\log(2) \) would give that relation).

So you want \( x \) to be deduced or possibly organizations or proper definitions would yield \( x \) connectively according to choices.

Would you have more elaboration on which log base is used if my last step or calculation didn't lay perfectly for your expectation?