Question

express the following as a single logarithm

ln(10 + x^7) + 1/2 lnx - ln (cosx)

Answer 1

\[\ln(10+x^7)+\frac{1}{2}\ln(x)-\ln(\cos(x)),\]\[\ln(10+x^7)+\ln(\sqrt{x})-\ln(\cos(x)),\]\[\ln(10+x^7+\sqrt{x}+\cos(x)).\]

Answer 2

My mistake.

Answer 3

oops

Answer 4

\[\ln\left(\frac{10+x^7+\sqrt{x}}{\cos(x)}\right).\]

Answer 5

\[\ln(10+x^7)+\ln(x^\frac{1}{2})-\ln(\cos(x)) \text{ using } \ln(x^r)=r \ln(x) \text{ property} \]
\[\ln(x^\frac{1}{2}(10+x^7))-\ln(\cos(x)) \text{ using } \ln(ab)=\ln(a)+\ln(b) \text{ property}\]
\[\ln(\frac{x^\frac{1}{2}(10+x^7)}{\cos(x)}) \text{ using } \ln(\frac{a}{b})=\ln(a)-\ln(b) \text{ property}\]

Answer 6

That's right! They multiply, not add. My mistake. Thanks myininaya. :)

Answer 7

Too many operations! ;)

Answer 8

thanks guys