REALLY really need an extra brain

**cowgirl69** · July 13th 2008, 03:12 PM

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.

**Mathstud28** · July 13th 2008, 03:26 PM

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.

$2e^{3x-1}=54$

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

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

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

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

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

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

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

$x^{5}=1728$

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

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