solve the following for x?

Question

2 to the 3x power = 10

Answer 1

2^(3x) = 10
Take log base ten of both sides:-
log 2^(3x) = 1
3x log 2 = 1
3x = 1 / log 2
x = (1/3) (1 / log 2)
x = 1.107

Answer 2

you have to use logs. not sure if you'll understand any of this because you didn't tell us if this was a calculus question or if it is just some extra credit for algebra, but:

2^3x = 10
ln(2^3x) = ln(10)
3x*ln(2) = ln(10)
3x = ln(10)/ln(2)
x = (ln(10)/ln(2))/3
i don't know any of these log values off the top of my head, so this is all I can give you. if you have an algebraic calculator on hand, then you can solve this part quickly.

Answer 3

2^3x = 10

log2^3x = log 10
3x is an exponent so it can be brought to the front.

=> 3xlog2 = 1 by the way Log 10 = 1

3x=1/log2

therefore X = 1/log2 divided by 3 i think it can be written as 1/3log2 im not too sure of quotient rules.

Answer 4

2^(3x) = 10
log-base2(2^(3x))= log-base2(10)
3x = log(10)/log(2) - - - change of base formula

x = 1/[3log(2)]

Answer 5

2^(3x) = 10

8^x = 10

x= log10 / log8 = 1/(3·log2) ~1.1073....

saludos.