Question

Express the following as a single logarithm.

ln(8+x^5)+(1/2)lnx−ln(cosx)

Answer 1

You'd just use some simple logarithm properties; even though the contents may be complicated, they still apply in the same way

a*ln(b) = ln(a^b)
ln(a) + ln(b) = ln(ab)
ln(a) - ln(b) = ln(a/b)

Answer 2

first property should be = ln(b^a) *

Answer 3

Originally this is what I had came up with:
\[(8+x^5)*(x^{1/2})/(\cos x)*\ln\]

Answer 4

other than the fact that the ln is out of place (the function 'ln' should contain that expression as an argument, not be multiplied to it), it looks correct to me.

\( \large{ ln(\frac{(8+x^5)(x^{1/2})}{cos(x)}) }\)

Answer 5

you could probably simplify it too by mutliplying the x^(1/2) through and changing 1/cos(x) to sec(x) and multiplying that through as well.