Question 4.4.5.7: Approximating a logarithm Whose Base is neither 10 Nor e App......

Remember, \log_{2}7 means “2 raised to what exponent equals 7?” Let y=\log_{2}7. Then 2^{y}=7. Because 2^{2}=4 and 2^{3}=8, the value of \log_{2}7 is between 2 and 3.

\ln2^{y}=\ln7                        Property (7)

y\ln2=\ln7                              Property (5)

y={\frac{\ln7}{\ln2}}                    Exact value

y\ \approx\ 2.8074                      Approximate value rounded to four decimal places