Question

Evaluate log(10^4 times 10^3)

Answer 1

To evaluate \( \log(10^4 \times 10^3) \), we can simplify the expression inside the logarithm first.

Using the property of exponents that states \( a^m \times a^n = a^{m+n} \):

\[
10^4 \times 10^3 = 10^{4+3} = 10^7
\]

Now we can rewrite the logarithm:

\[
\log(10^4 \times 10^3) = \log(10^7)
\]

Using the property of logarithms \( \log(a^b) = b \log(a) \), we can simplify this further:

\[
\log(10^7) = 7 \log(10)
\]

Since \( \log(10) = 1 \) (in base 10):

\[
7 \log(10) = 7 \times 1 = 7
\]

Thus, the final result is:

\[
\log(10^4 \times 10^3) = 7
\]