solve: 6^6x=124 Round to the nearest ten-thousandth

Question

campbell_st · Answer

do you know about logs...?

anonymous · Answer

Kinda sorta ! 
I got 0.8034 , am i right??

anonymous · Answer

I just am not sure how to round to the nearest ten thousandth

campbell_st · Answer

nope

here is my solution 

take the base 6 log of both sides

using the log law

$$\log _{a}a^b = b$$

then 
$$\log _{6}6^x = \log _{6}(124)$$


or $$6x = \log _{6}(124)$$

next use change of base to base e logs on the right hand side

$$6x = \frac{\ln(124)}{\ln(6)}$$

6x = 2.69025

divide by 6 gives 

x = 448375

you'll need to round the answer

anonymous · Answer

I diiiiiid it (: thank you SOooooo much !

campbell_st · Answer

oops I forgot a decimal point x = 0.448375