Find the solution of the exponential equation:
2^(2x+6) = 3^(x-39)
in terms of logarithms, or correct to four decimal places.

Question

Find the solution of the exponential equation:
2^(2x+6) = 3^(x-39)
in terms of logarithms, or correct to four decimal places.

misty1212 · Answer

HI!!

misty1212 · Answer

be prepared to do a fair amount of algebra here 
ready?

anonymous · Answer

yass

misty1212 · Answer

ok we start with 
$$(2x+6)\ln(2)=(x-39)\ln(3)$$ then solve for $x$ with the understanding that $\ln(2)$ and $\ln(3)$ are just some numbers (constants)

misty1212 · Answer

this is where the algebra comes in 
multiply out 
$$2\ln(2)x+6\ln(2)=\ln(3)x-39\ln(3)$$ good so far?

anonymous · Answer

yeah

misty1212 · Answer

k now we have to put all the x terms on one side of the equal sign, all the numbers on the other

misty1212 · Answer

$$2\ln(2)x-\ln(3)x=-6\ln(2)-39\ln(3)$$

misty1212 · Answer

next factor the $x$ out of the left hand side so we know what to divide by 
$$(2\ln(2)-\ln(3))x=-6\ln(2)-39\ln(3)$$

misty1212 · Answer

and finally divide 
$$x=\frac{-6\ln(2)-39\ln(3)}{2\ln(2)-\ln(3)}$$

misty1212 · Answer

now use a calculator, since you have to get it in decimal form

anonymous · Answer

ok thnx

misty1212 · Answer

on the other hand, since we have to use a calculator anyways, we might as well just solve it with a calculator

misty1212 · Answer

http://www.wolframalpha.com/input/?i=2%5E%282x%2B6%29+%3D+3%5E%28x-39%29 click on "approximate form" and you will see the answer

anonymous · Answer

i already did it and it was the right answer, thank you so much