# Thread: REALLY really need an extra brain

1. ## REALLY really need an extra brain

the last two problems of my homework for community college are tripping me up and I have been working on them ALL day my brain is on overload and it just won't crunch these numbers.. Help anyone>>??
The directions are to solve by hand and show all work !
problem #1) 2e^3x-1=54
problem #2) 2log4(x^4)-3log4(3x)=3

Both the 4's I made red because on my paper they are the bases .
The e I made blue because it's the natural slanted e.

2. Originally Posted by cowgirl69
the last two problems of my homework for community college are tripping me up and I have been working on them ALL day my brain is on overload and it just won't crunch these numbers.. Help anyone>>??
The directions are to solve by hand and show all work !
problem #1) 2e^3x-1=54
problem #2) 2log4(x^4)-3log4(3x)=3

Both the 4's I made red because on my paper they are the bases .
The e I made blue because it's the natural slanted e.
$\displaystyle 2e^{3x-1}=54$

$\displaystyle e^{3x-1}=27$

$\displaystyle 3x-1=\ln(27)=\ln(3^3)=3\ln(3)$

$\displaystyle 3x=3\ln(3)+1$

$\displaystyle x=\ln(3)+\frac{1}{3}$
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$\displaystyle 2\log_4(x^4)-3\log_4(3x)=3$

$\displaystyle \log_4(x^8)-\log_4((3x)^3)=3$

$\displaystyle \log_4\left(\frac{x^5}{27}\right)=3$

$\displaystyle \frac{x^5}{27}=64$

$\displaystyle x^{5}=1728$

$\displaystyle x=\sqrt[5]{1728}$