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

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vladianna | Student, Undergraduate | (Level 1) Honors

Posted August 8, 2011 at 8:34 PM via web

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

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted August 8, 2011 at 8:40 PM (Answer #1)

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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.

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