what is 2^x=10
solve for x please show steps

Question

regan · Answer

2=e^ln(2)
e^ln(2)x=10
ln(e^ln(2)x)=ln(10)
ln(2)x=ln(10)
x=ln(10)/ln(2)

anonymous · Answer

can you explain it please

regan · Answer

do you know what a logarithm is?

anonymous · Answer

not really

anonymous · Answer

is that what ln stands foor

regan · Answer

kind of.   ok imagine if we guess some values for x that will be close to 10
2^2=4
2^3=8
2^4=16
so we can imagine x lies in between 3 and 4     do you get that?

anonymous · Answer

yes

regan · Answer

so we need a method of finding x accurately. so we use logs.
logs shift us between bases and powers.  
we 'log' both sides    just as we would when using any function

regan · Answer

log(2^x)=log(10)
the law of exponents say log(2^x)=xlog(2)

regan · Answer

log(10)/log(2)=x
try it out on a calculator      the answer will be inbetween 3 and 4