SOLUTION: How do I solve 10^(x+4)=5^(2x), step by step?

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: How do I solve 10^(x+4)=5^(2x), step by step?      Log On


   

Question 372986: How do I solve 10^(x+4)=5^(2x), step by step?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
10%5E%28x%2B4%29=5%5E%282x%29 Start with the given equation.


ln%2810%5E%28x%2B4%29%29=ln%285%5E%282x%29%29 Take the natural log of both sides.


%28x%2B4%29ln%2810%29=2x%2Aln%285%29 Pull down the exponents using the identity ln%28x%5Ey%29=y%2Aln%28x%29%29


x%2Aln%2810%29%2B4%2Aln%2810%29=2x%2Aln%285%29 Distribute


4%2Aln%2810%29=2x%2Aln%285%29-x%2Aln%2810%29 Subtract x%2Aln%2810%29 from both sides.


4%2Aln%2810%29=x%282%2Aln%285%29-ln%2810%29%29 Factor out the GCF 'x' on the right side.


%284%2Aln%2810%29%29%2F%282%2Aln%285%29-ln%2810%29%29=x Divide both sides by 2%2Aln%285%29-ln%2810%29.


%284%28ln%282%29%2Bln%285%29%29%29%2F%282%2Aln%285%29-%28ln%282%29%2Bln%285%29%29%29=x Rewrite ln%2810%29 as ln%282%2A5%29=ln%282%29%2Bln%285%29


%284ln%282%29%2B4ln%285%29%29%2F%282%2Aln%285%29-ln%282%29-ln%285%29%29=x Distribute



%284ln%282%29%2B4ln%285%29%29%2F%28ln%285%29-ln%282%29%29=x Combine like terms.


So the real solution is x=%284ln%282%29%2B4ln%285%29%29%2F%28ln%285%29-ln%282%29%29


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim