Solve the equation using logarithms

Equation $$e^{2x+1.21} = 114\cdot 4^x$$ steps I've done so far.

• $2x + 1.21 = \ln(114) \cdot \ln(4) \cdot x$
• $x = (\ln(114) * \ln(4))/1.21$

I don't think I was allowed to move the $x$ from the right side to the left the way I did.

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1 Answer

It should be $$2x+1.21=\ln(114)+(\ln 4)x.$$ (Recall that if $a$ and $b$ are positive, then $\ln(ab)=\ln(a)+\ln(b)$.)

The rest should not be difficult. The displayed equation is linear in $x$. Bring the $x$ stuff to one side, and everything else to the other side.

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I got x(2 + (ln4)) = ln(114)-1.21 which lead me to my final answer x =(ln(114)/(ln(4)) -3.21 and I'm still getting a wrong answer. –  Tyler Zika Dec 5 '12 at 1:05
Yes, because it should be $x(2-\ln 4)=\ln(114)-1.21$, giving you $x=\dfrac{\ln(114)-1.21}{2-\ln 4}$. –  André Nicolas Dec 5 '12 at 1:07
Thank you! I need to refresh on my Algebra. Multiply and dividing polynomials is what I am lacking, right? –  Tyler Zika Dec 5 '12 at 1:12
There was a slip about logarithms, easy to make. There was later a problem with a linear equation kind of problem basically like $7x+1-=3x+49$, except with more complicated numbers. Ideally there should be no issue with these, they come up pretty often. –  André Nicolas Dec 5 '12 at 1:16