how to solve (8)3^x = 5 ?

Question

anonymous · Answer

$$(8)3^{x} = 5$$ , find x.

anonymous · Answer

@hartnn

hartnn · Answer

sure its , 
$8\times 3^x = 5$
?
take log on both sides, what do u get ?

kira_yamato · Answer

@hartnn Would it be more intuitive if we divide throughout by 8 first?

hartnn · Answer

yes, dividing by 8 is better step

anonymous · Answer

my answer is x = 1.62 , im not sure whether correct or not. @hartnn

hartnn · Answer

i don't think thats correct...how you got that value ?

hartnn · Answer

and you will get value in terms of log....
unless i misintrepret the question...

anonymous · Answer

$$\log 8  \ * log 3^{x} = \log 5$$
log 8 * x log 3 = log 5
x log 3 = log 5/log 8
x = log 5 / log 8 / log 3 
x = 1.62

these are my steps

anonymous · Answer

@jayjayokocha 
divide by 8 on both side.
take log base 10.
put value of log5,log5/8(=log5-log8).
do it, get ASNWER.

hartnn · Answer

you are not appling log rules correctly.

hartnn · Answer

lets first divide by 8 on both sides,
3^x = 5/8
now take log on both sides

hartnn · Answer

use, $\Large \log a^b=b \log a$

anonymous · Answer

so, now i got xlog3 = log 5 - log 8 , what's next ?

hartnn · Answer

just divide both sides by log 3 
and you would have got 'x'
thats it!

anonymous · Answer

answer is -0.428 ?

hartnn · Answer

YES.
thats the approximate answer :)

anonymous · Answer

just a quick one , 2^x = 5 
answer is x = 2.32 ? @hartnn

hartnn · Answer

yes, thats also correct :)