How could I find out the value of x
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The way you want to do this problem is using logarithms.
1. You see the problem: 2^x = 100. Your first objective is try to bring down the x from the exponent because as an exponent it is much harder to get the answer, and maybe even impossible
2. To bring down the exponent "x", you use logarithms. To do this you take log of both sides to make it look like this: log(2^x) = log(100).
3. This log will bring down the x to make the new equation look like this: log(2)*x = log(100).
4. Next step is really easy, just move all the non-variable constants to the other side of the equation to get the answer for x. x = log(100)/log(2).
5. The answer is: x = log(100)/log(2) or if you plug it in your calculator you'll get this decimal answer: 6.64
1. You see the problem: 2^x = 100. Your first objective is try to bring down the x from the exponent because as an exponent it is much harder to get the answer, and maybe even impossible
2. To bring down the exponent "x", you use logarithms. To do this you take log of both sides to make it look like this: log(2^x) = log(100).
3. This log will bring down the x to make the new equation look like this: log(2)*x = log(100).
4. Next step is really easy, just move all the non-variable constants to the other side of the equation to get the answer for x. x = log(100)/log(2).
5. The answer is: x = log(100)/log(2) or if you plug it in your calculator you'll get this decimal answer: 6.64
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2^x = 100
log 2^x = log 100
x log 2 = log 100
x = log 100 / log 2 <-- exact answer
x = 6.643856 <-- decimal approximation using a scientific calculator
log 2^x = log 100
x log 2 = log 100
x = log 100 / log 2 <-- exact answer
x = 6.643856 <-- decimal approximation using a scientific calculator
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Divide each side by 2. So x=50