MHB What is the Solution for $5^x+2=12$?

[karush]

Solve $5^x+2=12$
$5^x=10\implies x\ln(5)=\ln(10)\implies x=\dfrac{\ln(10)}{\ln(5)}\approx \boxed{1.4307}$

ok i think this is ok but typos or better steps maybe

 

[topsquark]

Solve $5^x+2=12$
$5^x=10\implies x\ln(5)=\ln(10)\implies x=\dfrac{\ln(10)}{\ln(5)}\approx \boxed{1.4307}$

ok i think this is ok but typos or better steps maybe

Looks good. The only possible improvement I might suggest is to use [math]log_5[/math] instead of ln (then [math]x = log_5(10)[/math]) but in practical terms most calculators don't have a key to evaluate [math]log_5(10)[/math] so I'd use ln, too.

-Dan

 

[Kansas Boy]

You solved $5^x+ 2= 12$ but the title of this thread was "Solve $5^x+ 2= 126$". Which is it?

 

[Kansas Boy]

If the problem is actually $5^x+ 2= 126$ then $5^x= 124$, $log(5^x)= x log(5)= log(124)$ so $x= \frac{log(124)}{log(5)}$. Since $5^3= 125$ x will be a little less than 3. Using a calculator, x is about 2.99500933 .

 

[karush]

You solved $5^x+ 2= 12$ but the title of this thread was "Solve $5^x+ 2= 126$". Which is it?

sorry I edited the title to what I solved