1. ## logs!!

4 times 2^x = 8 times 5^x solve for x

2. Originally Posted by lbj2322
4 times 2^x = 8 times 5^x solve for x
$4(2^x) = 8(5^x)$

Since both sides are equal, if we take the log of both sides, they remain equal. Assume the common (base 10) log

$log (4(2^x)) = log (8(5^x))$

Hopefully you know the properties of logs, and know how to re-write a log of a product:

$log 4 + log 2^x = log 8 + log 5^x$

Another property of logs lets you move the exponent

$log 4 + x log 2 = log 8 + x log 5$

We've now cleared the exponents. You should be able to move all the x's to the same side, and the other terms to the other side, and use basic algebra to get x by itself. Then use your calculator to compute the $log_{10}$ values.

Note also, you can simplify the original equation by first dividing both sides by 4.