Solve for x : 3^(2x-1)=5^(x+1)

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giorgiana1976
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We'll take natural logarithms both sides:
ln `3^(2x-1)` = ln `5^(x+1)`
Now, we'll use the power property of logarithms:
(2x-1)*ln 3 = (x+1)*ln 5
We'll remove the brackets:
2x*ln 3 - ln 3 = x*ln 5 + ln 5
We'll move all the terms in x to the left side:
(2ln 3)*x - (ln 5)*x = ln 5 + ln 3
We'll factorize by x:
x(ln 9 - ln 5) = ln 5 + ln 3
We'll use the quotient property to the left side and product property to the right side:
x*ln(9/5) = ln(5*3)
0.5877*x = 2.7080
x = 2.7080/0.5877
x = 4.6078
The solution of the equation is x = 4.6078.
Posted by giorgiana1976 on August 8, 2011 at 8:40 PM (Answer #1)

giorgiana1976
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We'll take natural logarithms both sides:
ln `3^(2x-1)` = ln `5^(x+1)`
Now, we'll use the power property of logarithms:
(2x-1)*ln 3 = (x+1)*ln 5
We'll remove the brackets:
2x*ln 3 - ln 3 = x*ln 5 + ln 5
We'll move all the terms in x to the left side:
(2ln 3)*x - (ln 5)*x = ln 5 + ln 3
We'll factorize by x:
x(ln 9 - ln 5) = ln 5 + ln 3
We'll use the quotient property to the left side and product property to the right side:
x*ln(9/5) = ln(5*3)
0.5877*x = 2.7080
x = 2.7080/0.5877
x = 4.6078
The solution of the equation is x = 4.6078.
Posted by giorgiana1976 on August 8, 2011 at 8:40 PM (Answer #1)