1. ## Exponents and Logs

Why is the 5 in this equation, I can't multiply the 2 and 5, some of this math is so confusing

$\displaystyle 2(5)^x=7^{x+1}$

2. Originally Posted by nuckers
Why is the 5 in this equation, I can't multiply the 2 and 5, some of this math is so confusing

$\displaystyle 2(5)^x=7^{x+1}$
The 5 is the base of the exponential. You can still take logs and use the relevant log laws.

Hint: $\displaystyle \log(2\cdot 5^x) = \log(2) + \log(5^x)$

3. Originally Posted by nuckers
$\displaystyle 2(5)^x=7^{x+1}$
That equation is equivalent to $\displaystyle \left( {\frac{5}{7}} \right)^x = \frac{7}{2}$ which has solution $\displaystyle x = \frac{{\log (7) - \log (2)}}{{\log (5) - \log (7)}}$

4. Originally Posted by Plato
That equation is equivalent to $\displaystyle \left( {\frac{5}{7}} \right)^x = \frac{7}{2}$ which has solution $\displaystyle x = \frac{{\log (7) - \log (2)}}{{\log (5) - \log (7)}}$
I'm totally confused how you came up with that. I did screw up and put a 7 in the equation, it's supposed to be $\displaystyle 3^{x+1}$

5. Originally Posted by nuckers
I'm totally confused how you came up with that. I did screw up and put a 7 in the equation, it's supposed to be $\displaystyle 3^{x+1}$
$\displaystyle 2 \cdot 5^x = 3^{x + 1}$ is equivalent to $\displaystyle \left( {\frac{5}{3}} \right)^x = \frac{3}{2}$ which has solution $\displaystyle x = \frac{{\log (3) - \log (2)}}{{\log (5) - \log (3)}}$
To see how that works divide both sides by $\displaystyle 3^x$ and also by $\displaystyle 2$.
Note that $\displaystyle \frac{{5^x }}{{3^x }} = \left( {\frac{5}{3}} \right)^x$.

6. Originally Posted by Plato
$\displaystyle 2 \cdot 5^x = 3^{x + 1}$ is equivalent to $\displaystyle \left( {\frac{5}{3}} \right)^x = \frac{3}{2}$ which has solution $\displaystyle x = \frac{{\log (3) - \log (2)}}{{\log (5) - \log (3)}}$
To see how that works divide both sides by $\displaystyle 3^x$ and also by $\displaystyle 2$.
Note that $\displaystyle \frac{{5^x }}{{3^x }} = \left( {\frac{5}{3}} \right)^x$.
Ok, i understand it now, thanks so much for the help, i appreciate it