SOLUTION: If 6^[1-(2/x)] = 3 Find 2^x

Question 1209382: If 6^[1-(2/x)] = 3
Find 2^x
Found 3 solutions by math_tutor2020, Edwin McCravy, greenestamps:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Let's solve for x.
6^[ 1-(2/x) ] = 3
log( 6^[ 1-(2/x) ] ) = log(3)
(1-2/x)*log(6) = log(3)
1-2/x = log(3)/log(6)
(x-2)/x = log(3)/log(6)
(x-2)*log(6) = log(3)*x
x*log(6)-2*log(6) = log(3)*x
x*log(6)-log(3)*x = 2*log(6)
x*(log(6)-log(3)) = 2*log(6)
x*log(6/3) = 2*log(6)
x*log(2) = log(6^2)
x = log(36)/log(2)
x = log₂(36)
Then,
2^x = 2^[ log₂(36) ] = 36

Or after you determine x you could say,
y = 2^x
log(y) = log(2^x)
log(y) = x*log(2)
log(y) = (log(36)/log(2))*log(2)
log(y) = log(36)
y = 36
2^x = 36

Answer by Edwin McCravy(20065)   (Show Source): You can put this solution on YOUR website!

Raise both sides to the -1 power Take log base 2 of both sides: Raise 2 to the power of each side Answer: 36 Edwin

Answer by greenestamps(13216)   (Show Source): You can put this solution on YOUR website!

A solution without using logarithms....

Raise each side of the equation to the power x

Rewrite the left side as the product of powers of 2 and 3

Multiply both side by 2^2

ANSWER:

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A similar solution without using logarithms....

Raise each side to the power x

Take reciprocals of each side

ANSWER:

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