Question

Find the exact value of x to satisfy the equation
(3^x)(4^(2x+1))=6^(x+2)

Answer 1

Give your answer in the form lna/lnb

Answer 2

\[x=\frac{\text{Log}[9]}{\text{Log}[8]} \]

Answer 3

To do that will you simplify the left side then take the log of both sides?

Answer 4

Initially the Mathematica result was:\[x\to \frac{2 \text{Log}[3] \text{Log}[6]}{(\text{Log}[2]+\text{Log}[3]) (\text{Log}[3]+2 \text{Log}[4]-\text{Log}[6])} \]The final result came from a "FullSimplify" of the complex fraction.

Answer 5

\[x=(2\log6-\log4)
|dw:1314748005748:dw
|(\log3+2\log4-\log6)\]

Answer 6

** \[x=(2\log6-\log4)/(\log3+2\log4-\log6)\]

Answer 7

The numeric value of the above fraction is:\[\frac{2 \log (6)-\log (4)}{\log (3)+2 \log (4)-\log (6)}\text{//}N\text{ }\to \text{ }1.05664 \]\[\frac{2 \log (6)-\log (4)}{\log (3)+2 \log (4)-\log (6)}\text{//}\text{FullSimplify}\text{ }\to \frac{\text{Log}[9]}{\text{Log}[8]} \]\[\frac{\text{Log}[9]}{\text{Log}[8]}\text{//}N\text{ }\to \text{ }1.05664 \]

Answer 8

Could you demonstrate for me how you simplified the expression?

Answer 9

No. The numerator simplified by it's self is Log(9) and the denominator simplifies to Log(8). Frankly I never liked logarithms when I was in school.

Answer 10

What is the first few steps. I can't get myself there without canceling out Log6with l

Answer 11

Log6