solve the exponential equation

Question

1.) 5^2x-3=7^x+9

 

2.) 2e^2x-11e^x+5

 

Answer 1

2) 2e^(2x)-11e^x+5=0 is the problem (just my guess !!!)

    let n=e^x

    2n^2-11n+5=0

    factor

    (2n-1)(n-5)=0

    2n-1=0

    2n=1

    n=1/2

    n=e^x

    e^x=1/2

    x=ln(1/2)

    x=-0.69314718056

    n-5=0

    n=5

    n=e^x

    e^x=5

    x=ln(5)

    x=1.60943791243

 

 

Answer 2

1). 5^2x-3 = 7^x-9

 

log(5^2x-3) = log(7^x-9)

 

(2x-3)log5 = (x-9)log7

 

2xlog5 - 3log5 = xlog7 - 9log7

 

2xlog5 - xlog7 = 3log5 - 9log7

 

x(2log5 - log7) = 3log5 - 9log7

 

x = (3log5 - 9log7)/(2log5 - log7) ≈ -9.96

 

2). There is no equation to solve.