How can you solve this without guessing?

Question

waheguru · Answer

2^x=64

uri · Answer

$$2^x?$$

waheguru · Answer

two to the power of something is 64, but how do you answer that mathematically

yes @uri

uri · Answer

Oh so 2*2*2*2*2*2=64

nurali · Answer

$$2^x=64$$

$$2^x=2^6$$

$$x=?$$

uri · Answer

2^6=64

ivettef365 · Answer

log2(64)

waheguru · Answer

I know that but how do you get it without guessing, like moving the x or something

uri · Answer

It's common sense..

waheguru · Answer

i know... but sometimes there are big numbers like in the thousands

ivettef365 · Answer

http://logbase2.blogspot.com/2008/08/log-calculator.html

uri · Answer

Aren't you allowed to use calculator?

ivettef365 · Answer

use log base 2 times 64

waheguru · Answer

so 2log64? @ivettef365

thomaster · Answer

$\sf\large p^x=q \to x=p~log(q)$
but you'd need a calculator for that

waheguru · Answer

with the log button i am getting 3.6?     2log64

jdoe0001 · Answer

$\bf 2^x=64\
\textit{log cancellation rule of } log_aa^x = x\
log_2{2^x} = log_264 \implies x = log_264\
\textit{change of base rule } log_ab  = \cfrac{log_cb}{log_ca}\
x = \cfrac{log_{10}64}{log_{10}2}$

thomaster · Answer

yes you need to use this:

$\large\sf a~log(b)=\dfrac{log(b)}{log(a)}$

$\large\sf \dfrac{log(64)}{log(2)}=6$

waheguru · Answer

Thanks to everyone for the help

anonymous · Answer

use logs

mathstudent55 · Answer

|dw:1375732867756:dw|