X in exponent on both sides, can't make bases the same

Printable View

July 29th 2010, 12:36 PM
jimmy1

X in exponent on both sides, can't make bases the same

Help:

$7^-^4^x = 2^1^+^3^x$
I should take the ln of both sides, right...?
$-4x ln 7 = (1+3x) ln 2$

How do I simplify?
July 29th 2010, 12:43 PM
Ackbeet

I would distribute out the RHS first. Your goal, as always is to get the terms with x's on one side, and all the other terms on the other.
July 29th 2010, 12:43 PM
bobak

You don't want to simplify, you want to solve the equation. Step back and look at what you have written, remember that ln7 and ln2 are just numbers.
July 29th 2010, 12:48 PM
eumyang

Quote:

Originally Posted by jimmy1

Help:

$7^-^4^x = 2^1^+^3^x$
I should take the ln of both sides, right...?
$-4x ln 7 = (1+3x) ln 2$

How do I simplify?

$\begin{aligned} 7^{-4x} &= 2^{1 + 3x} \\ -4x \ln 7 &= (1+3x) \ln 2 \\ -4x \ln 7 &= \ln 2 + 3x \ln 2 \\ 3x \ln 2 + 4x \ln 7 &= -\ln 2 \\ x(3\ln 2 + 4\ln 7) &= -\ln 2 ... \\ \end{aligned}$

Can you finish?

All times are GMT -8. The time now is 12:15 AM.