5) In this one, let's take the logarithm on both sides:
[tex]\begin{gathered} 10^x=315 \\ \log_{10}10^x=\log_{10}315 \\ x=2.498 \end{gathered}[/tex]6) Let's begin this exponential equation by simplifying it whenever possible:
[tex]\begin{gathered} 2*10^x=800 \\ \frac{2*10^x}{2}=\frac{800}{2} \\ 10^x=400 \end{gathered}[/tex]Note that we cannot rewrite 400 as a power of base 10, so let's resort to the logarithm:
[tex]\begin{gathered} \log_{10}10^x=\log_{10}400 \\ x=2.60 \end{gathered}[/tex]Note that according to the property of the logarithm, we can tell that log_10(10)^x is equal to x
7)
[tex]\begin{gathered} 10^{\left(1.2x\right)}=4000 \\ \log_{10}10^{1.2x}=\log_{10}4000 \\ 1.2x=3.60 \\ \frac{1.2x}{1.2}=\frac{3.6}{1.2} \\ x=3.00 \end{gathered}[/tex]Note that in this case, we had to take the logarithms on both sides right away.
8)
[tex]\begin{gathered} 7*10^{0.5x}=70 \\ \frac{7*10^{0.5x}}{7}=\frac{70}{7} \\ 10^{0.5x}=10 \\ 0.5x=1 \\ \frac{0.5x}{0.5}=\frac{1}{0.5} \\ x=2 \end{gathered}[/tex]Note that in this case, after dividing both sides by 7 we ended up with two powers of base 10.
