Solve for x. (25e^0.1x)/(e^(0.1x) + 3) = 10

Question

e^2.5x / (e^(0.1x) + 3) = 10
e^(2.5x - 0.1x) + 1/3 = 10
e^2.4x = 29/3
ln^(e^(2.4x)) = ln(29/3)
2.4x = ln(29/3)
x = 0.945

Is that correct?

Answer 1

Let e^.1 x = y
25 y /(y+3) = 10
25 y = 10 y + 30
15 y = 30
y = 2
so
e^.1 x = 2
ln e^.1x = ln 2
.1 x = ln 2
x = 10 ln 2
= 6.931

Answer 2

Express the given quantity as a single logarithm.
ln(1+x^8)+ln(x)- ln(sin(x))