Question

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

Answer 1

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)

Answer 2

can you explain it please

Answer 3

do you know what a logarithm is?

Answer 4

not really

Answer 5

is that what ln stands foor

Answer 6

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?

Answer 7

yes

Answer 8

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

Answer 9

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

Answer 10

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