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irakobra [83]
4 years ago
7

Please help solve this:

1} = 100" alt=" 3^{x + 1} = 100" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
IrinaVladis [17]4 years ago
4 0
Remember, you can do anything to an equaiton as long as you do it to both sides

also
log(a^x)=xlog(a)
andln(x)=log_e(x)
ok
if no base is stated, assume log=log_{10}
I'm going to use ln instead of log because ln is easier to find on a calculator

3^{x+1}=100
take ln of both sides
ln(3^{x+1})=ln(100)
(x+1)ln(3)=ln(100)
xln(3)+1ln(3)=ln(100)
minus ln(3) both sides
xln(3)=ln(100)-ln(3)
divide both sides by ln(3)
x=\frac{ln(100)}{ln(3)}-1

or if you wanted to use log base 10
3^{x+1}=100
take log both sides
log(3^{x+1})=log(100)
log(3^{x+1})=2
(x+1)log(3)=2
xlog(3)+log(3)=2
minus log(3) both sides
xlog(3)=2-log(3)
divide both sides by log(3)
x=\frac{2}{log(3)}-1



so
x=\frac{ln(100)}{ln(3)}-1
or if you wanted log
x=\frac{2}{log(3)}-1
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