If something to the power of x is 2, how do you calculate x?

Question

well my problem is (1.045)[ttpo]x = 2

i know i was taught a way to do it once but now it has escaped me. i thing it has something to do with log.

btw I don't want the answer to the problem, I want to know how to get to the answer.

Answer 1

(1.045)^x = 2

x ln(1.045) = ln(2)

x = ln(2)/ln(1.045)

x = 15.75

Answer 2

Take a log of the base of the number being raised to the x power.

log base 1.045 (1.045^x)=log base 1.045(2)

                                   x=log base 1.045(2)

Answer 3

Generally people use ^ to mean "to the power of"

1.045^x = 2

To solve this, take the log of both sides:

log(1.045^x) = log(2)

Then remember this rule of logs --> log(a^x) = x * log(a).

Use that to bring the x out in front.

x log(1.045) = log(2)

Divide both sides by log(1.045) to isolate x:

x = log(2) / log(1.045)

Now get out your calculator... (Hint:  x is a value between 15 and 16).

Answer 4

For exercises of this type, u should always use log base 10 to work it out........generally, log to the base of 10 is written as lg, another thing is : lg x^a = a . lg a       , you bring the power to the front.

note: the point ( . ) denotes multiplied by.........denotes 'times', ok......

Hence: you introduce lg to the right and left side of the equation:

lg 1.045^x = lg 2

You bring the power 'x' to the front:

x . lg 1.045 = lg 2

U make 'x' subject of formula:

x = lg 2 / lg 1.045

   = ans

Just calculate it using a calculator.......