Question

URGENT:

suppose that ln5=a and ln11=b. Use properties of logarithms to write the logarithm in terms of a and b. ln 5sqrt55

Answer 1

The phrase asked:
`\ln5√(55)`

if ln5=a and ln11=b:

`\ln5√(55) =\\\\ \ln5+\ln(55)^{(1)/(2)}=\\\\\\ \ln5+(1)/(2)(\ln55)=\\\\\\ \ln5+(1)/(2)(\ln5.11)=\\\\\\ \ln5+(1)/(2)(\ln5+\ln11)=\\\\\\ a+(1)/(2)(a+b)= (1)/(2)(3a+b)`

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theorem 1:

`\ln(x.y)= \ln x + \ln y`

theorem 2:

`\log_a{x^n} = n \cdot \log_a{x}`