If 10^logx=1/10^32

Question

, 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:

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