Question

If 10^logx=1/10^32
, what is the value of x?(1 point)
Responses

10^32
10 superscript 32 baseline

−32
negative 32

10^−32
10 superscript negative 32 baseline

32

Answer 1

To solve the equation \( 10^{\log x} = \frac{1}{10^{32}} \), we can rewrite \(\frac{1}{10^{32}}\) as \(10^{-32}\). Thus, the equation becomes:

\[
10^{\log x} = 10^{-32}
\]

Since the bases are the same, we can set the exponents equal to each other:

\[
\log x = -32
\]

To solve for \(x\), we can rewrite the logarithmic equation in its exponential form:

\[
x = 10^{-32}
\]

So, the value of \(x\) is:

\[
\boxed{10^{-32}}
\]