To solve for [tex]\( h \)[/tex] in the equation [tex]\(0.0027 = 2.7 \times 10^h\)[/tex], we can follow these steps:
1. Isolate the exponential term [tex]\( 10^h \)[/tex]:
Begin by dividing both sides of the equation by 2.7 to isolate the [tex]\( 10^h \)[/tex] term.
[tex]\[
\frac{0.0027}{2.7} = \frac{2.7 \times 10^h}{2.7}
\][/tex]
Simplifying the right-hand side, we get:
[tex]\[
\frac{0.0027}{2.7} = 10^h
\][/tex]
2. Simplify the fraction:
Calculate the value of the fraction:
[tex]\[
\frac{0.0027}{2.7} = 0.001
\][/tex]
Therefore, the equation becomes:
[tex]\[
0.001 = 10^h
\][/tex]
3. Convert to logarithmic form:
To solve for [tex]\( h \)[/tex], take the base-10 logarithm (logarithm to base 10) of both sides:
[tex]\[
\log_{10}(0.001) = \log_{10}(10^h)
\][/tex]
Using the logarithm property [tex]\( \log_{10}(10^h) = h \)[/tex]:
[tex]\[
\log_{10}(0.001) = h
\][/tex]
4. Evaluate the logarithm:
Recall that [tex]\( 0.001 = 10^{-3} \)[/tex]. Therefore:
[tex]\[
\log_{10}(10^{-3}) = -3
\][/tex]
So, [tex]\( h \)[/tex] is:
[tex]\[
h = -3
\][/tex]
Therefore, the value of [tex]\( h \)[/tex] in the equation [tex]\( 0.0027 = 2.7 \times 10^h \)[/tex] is [tex]\(-3\)[/tex].
