## anonymous 3 years ago 4^x=12

1. anonymous

$b^x=A\iff x=\frac{\ln(A)}{\ln(b)}$

2. anonymous

this is sometimes called the "change of base" formula in your case $$A=12,b=4$$

3. anonymous

Log both sides so u get log 4^x =log 12. therefore by law of logs x log 4 = log 12. so x=log 12/log 4...

4. anonymous

thank you so much

5. anonymous

$\log 4^{x} = \log 12$ $x \log 4 = \log 12$ $x = \log 12\div \log 4$