Answer :
We are asked to evaluate
[tex]$$
\log_{10}\left(10^{-101}\right).
$$[/tex]
Step 1: Recall the logarithm property that if you have [tex]$\log_b\left(b^x\right)$[/tex] then the result is simply [tex]$x$[/tex]. This is because the logarithm function is the inverse of the exponential function.
Step 2: Applying this property with [tex]$b=10$[/tex] and [tex]$x=-101$[/tex], we get
[tex]$$
\log_{10}\left(10^{-101}\right) = -101.
$$[/tex]
Thus, the correct choice is
(D) [tex]$-101$[/tex].
[tex]$$
\log_{10}\left(10^{-101}\right).
$$[/tex]
Step 1: Recall the logarithm property that if you have [tex]$\log_b\left(b^x\right)$[/tex] then the result is simply [tex]$x$[/tex]. This is because the logarithm function is the inverse of the exponential function.
Step 2: Applying this property with [tex]$b=10$[/tex] and [tex]$x=-101$[/tex], we get
[tex]$$
\log_{10}\left(10^{-101}\right) = -101.
$$[/tex]
Thus, the correct choice is
(D) [tex]$-101$[/tex].
