Wednesday
October 1, 2014

Homework Help: Math

Posted by Anonymous on Monday, September 20, 2010 at 9:21pm.

My question says:
Find the exact alue of x for which (4^x)*(5^[4x+3])=(10^[2x+3])

I can't seem to come to a solution.
We're reviewing last year's lessons, so change of base and logarithmic expressions are what we're going over right now.

Here's what I've done so far:

(4^x)*(5^[4x+3])=(10^[2x+3])
log both sides
log[(4^x)*(5^[4x+3])]=log[(10^[2x+3])]
(xlog4)+([4x+3]log5)=([2x+3]log10)
since log10=1
(xlog4)+([4x+3]log5)=(2x+3)

Have I started correctly? Where do I go from here? Please be detailed, I want to understand this.

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