Question 1117690

So I have to solve this equation by using logarithms.  I am so lost. 

2.5^x=34.1^(2x+7)
<pre>TOTALLY IGNORE the suggestion by that person to CONVERT the decimals to fractions. That doesn't make ANY SENSE, at all!!
{{{matrix(1,3, 2.5^x, "=", 34.1^(2x + 7))}}}
{{{matrix(1,3, log ((2.5^x)), "=", log ((34.1)^(2x + 7)))}}} ------ Taking log of both sides
x log (2.5) = (2x + 7) * log (34.1)
{{{matrix(1,3, x/(2x + 7), "=", log ((34.1))/log((2.5)))}}}
{{{matrix(1,3, x/(2x + 7), "=", 3.8517)}}}
3.8517(2x + 7) = x ------- Cross-multiplying
7.7034x + 26.9619 = x
26.9619 = x - 7.7034x
26.9619 = - 6.7034x
{{{highlight_green(matrix(1,5, x, "=", 26.9619/(- 6.7034), "=", - 4.022))}}}