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

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giorgiana1976's profile pic

Posted on

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.

tonys538's profile pic

Posted on

The equation 3^(2x-1)=5^(x+1) has to be solved for x.

It is only possible to solve the given equation by the use of logarithm and an approximate result can be obtained.

Take the log to base 10 of both the sides of the equation.

log(3^(2x-1))=log(5^(x+1))

Use the property of logarithm log a^b = b*log a

(2x - 1)*log 3 = (x + 1)*log 5

(2x - 1)/(x + 1) = log 5/log 3

Now the value of log 5/log 3 is approximately 1.464973521

2x - 1 = (x +1)*1.464973521

x*(2 - 1.464973521) = 1.464973521 + 1

x*0.5350364793 = 2.464973521

x = 2.464973521/0.5350364793

x = 4.60711300325

The solution of the equation is x = 4.60711300325

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