3.11 The natural logarithm
Find the value of each of the following correct to four decimal places:
\ln 94
\ln 0.042
\ln 78^{4}
\ln \left( 18 \times 35\right)
Consider x=\ln 31. Find the value of x, correct to two decimal places.
Use the properties of logarithms to express each of the following without any powers or surds:
Use the properties of logarithms to rewrite - 2 \ln x with a positive power.
Rewrite each of the following as the sum and difference of logarithms:
Rewrite each of the following expressions as a single logarithm:
\ln 3 + \ln 5
\ln 24 - \ln 4
\ln 8 - \ln 32
\ln \left( 3 x\right) + \ln \left( 5 y\right)
Which expression is equivalent to 2 \ln \left( 7 x\right) for x > 0?
\ln \left( 14 x\right)
\ln 14 + \ln x
\ln 49 + \ln x
\ln \left( 49 x^{2}\right)
Simplify:
Evaluate each of the following expressions:
\ln e^{3.5}
\ln e^{4}
\sqrt{6} \ln \left(e^{\sqrt{6}}\right)
\ln \left(\dfrac{1}{e^{2}}\right)