SOLUTION: I think this should be in the log category. Any help will be appreciated!
Let x be the solution to 4^(1-x)=8^x in simplest form. What is the value of x?
The answer is 2/5, bu
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Question 1028400: I think this should be in the log category. Any help will be appreciated!
Let x be the solution to 4^(1-x)=8^x in simplest form. What is the value of x?
The answer is 2/5, but I need help getting there.
Found 2 solutions by robertb, rothauserc:
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
==> 2(1-x) = 3x
==> 2-2x = 3x
==> 2=5x ==> x = 2/5.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
4^(1-x) = 8^x
:
Take the natural logarithm of both sides and use the identity log(a^b) = b log(a)
:
2log(2)(1-x) = 3log(2)x
:
Expand out terms of the left hand side:
2log(2)-2log(2)x = 3log(2)x
:
Subtract 3xlog(2)+2log(2) from both sides:
-5log(2)x = -2log(2)
:
Divide both sides by -5log(2)
:
****************
x = 2/5
****************
:
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