solve the equation 2exponent3x=3exponent2x+1?

Question

trying to get the answer the 3x is exponent of 2 = 2x+1 is an exponent of 3

Answer 1

2^3x = 3^(2x+1)

so

log(2^3x) = log[3^(2x+1)]

3x log(2) = (2x+1) log(3)

3x log(2) = 2x log(3) + log(3)

3x log(2) - 2x log(3) = log(3)
x(3 log(2) - 2 log(3)) = log(3)

x = log(3) / [3 log(2) - 2 log(3)]
= log(3) / [ log(2^3) - log(3^2)]
= log(3) / log (8 / 9)
= 0.4771 / -0.0512
= -9.3274

Answer 2

2^3x = 3^(2x+1)

ln(2^3x) = ln(3^(2x+1))
3x(ln2) = (2x + 1)(ln3)
3x(ln2) - 2x(ln3) = ln3
x(3ln2 - 2ln3) = ln3
x = ln3/(3ln2 - 2ln3)

I don't have a calculator on me right now, you can get a number answer by plugging it into your calculator if you want to.

Answer 3

2^(3x) = 3^(2x+1)

"Logarithm" both sides; any base, as long as you use the same base throughout.

3x*ln(2) = (2x+1)*ln(3)
3x*ln(2) = 2x*ln(3) + ln(3)
3x*ln(2) - 2x*ln(3) = ln(3)
x[3ln(2)-2ln(3)] = ln(3)
x = ln(3) / [3ln(2)-2ln(3)]