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log equation? Help Please?
2*3^x=5*2^x
Read as 2 times 3 to the x power, equals 5 times 2 to the x power.
The answer I got is x=log2/(log(3) - log(5/2))
Read as x equals the log of 2 divided by the log of 3 minus the log of the fraction 5 over 2.
Am i correct? I am confused because the decimal number i get when plugging this answer into the calculator is not making each side of the equation equal when checking my answer.
Please explain your answer if I am wrong. Thanks so much I will reward with 10 points. thanks guys
3 Answers
- AdmireLv 78 years ago
3^x = 5*2^x /2
3^x = 5*2^(x-1)
log 3^x = log 5 + log 2^(x-1)
xlog 3 = log 5 + (x-1)log 2
xlog 3 = log 5 + xlog 2 - log 2
xlog 3 - x log 2 = log 5 - log 2
x(log 3 - log 2) = log 5 - log 2
x = (log 5 - log 2)/(log 3 - log 2)
- SteveLv 78 years ago
2*3^x=5*2^x
3^x/2^x = 5/2
[3/2]^x = 5/2
x*ln[3/2] = ln[5/2]
x = ln[5/2]/ln[3/2] = 2.25985, which gives the same value for both sides.....
