## anonymous 4 years ago please show all steps and simplify 2^(logbase2 3+logbase2 5)??

1. anonymous

step one: post question to openstudy.com

2. ash2326

$$2^ { log 3+ log 5}$$ log is to the base 2 log A + Log B= log AB and $x^{log (y)}= y$ is log is to the base x so $2^{ log 15}$ = $$log 15$$

3. anonymous

@ash: everything except that the last step should be = 15. Compare to: $2^{\log_2 3 + \log_2 5} = 2^{\log_2{3}}\cdot2^{\log_2{5}}$ $2^{\log_2{3}}\cdot2^{\log_2{5}} = 3 \cdot 5 = 15$

4. ash2326

sorry i made mistake it's 15