Question

Solve 2^(2x+1)=20

Answer 1

try taking the ln of log of both sides

Answer 2

Should I simplify it first?

Answer 3

There is nothing to simplify before taking the log

Answer 4

I used the quotient law then I am stuck

Answer 5

what did you get when you log both sides?

Answer 6

2^(2x+1) = 20

yes simplify first, cancel a factor of 2

2^(2x) = 10

then use an index law on the lefthand side

(2^2)^x = 10

Answer 7

when you have

b^x = 10

take the log of both sides (to base b)

x = log_b (10)
= ln 10 / ln b (change of base formula)

and use another log law to simplify this

Answer 8

\[2^{2x+1}=10\]\[(2x+1)\ln 2=\ln 10\]\[2x+1=\frac{ \ln10 }{\ln2 }\]\[x=\frac{ 1 }{ 2 }(\frac{ \ln10 }{\ln2 }-1)\]