Question 63487
<pre><font face = "Tahoma" size = 5 color = "darkgreen"><b>
Solve:

5<sup>x+3</sup> = 6<sup>x</sup>

Take the natural log of both sides:

ln(5<sup>x+3</sup>) = ln(6<sup>x</sup>)

Use the rule

ln(A<sup>N</sup>) = N·ln(A) on each side:

(x + 3)ln(5) = x·ln(6)

Let ln(5) = A and let ln(6) = B

(x + 3)A = xB

A(x + 3) = Bx

Ax + 3A = Bx

Ax - Bx = -3A

x(A - B) = -3A

Divide both sides by (A - B)

x = -3A/(A - B)

Now replace A by ln(5) and B by ln(6)

x = -3·ln(5)/( ln(5) - ln(6) )

Get calculator:

x = 26.38240736

Edwin</pre></font>