remember, you can do anything to an equaiton as long as you do it to both sides
also [tex]log(a^x)=xlog(a)[/tex] and[tex]ln(x)=log_e(x)[/tex] ok if no base is stated, assume log=[tex]log_{10}[/tex] I'm going to use ln instead of log because ln is easier to find on a calculator
[tex]3^{x+1}=100[/tex] take ln of both sides [tex]ln(3^{x+1})=ln(100)[/tex] [tex](x+1)ln(3)=ln(100)[/tex] [tex]xln(3)+1ln(3)=ln(100)[/tex] minus ln(3) both sides [tex]xln(3)=ln(100)-ln(3)[/tex] divide both sides by ln(3) [tex]x=\frac{ln(100)}{ln(3)}-1[/tex]
or if you wanted to use log base 10 [tex]3^{x+1}=100[/tex] take log both sides [tex]log(3^{x+1})=log(100)[/tex] [tex]log(3^{x+1})=2[/tex] [tex](x+1)log(3)=2[/tex] [tex]xlog(3)+log(3)=2[/tex] minus log(3) both sides [tex]xlog(3)=2-log(3)[/tex] divide both sides by log(3) [tex]x=\frac{2}{log(3)}-1[/tex]
so [tex]x=\frac{ln(100)}{ln(3)}-1[/tex] or if you wanted log [tex]x=\frac{2}{log(3)}-1[/tex]
