Mathematics: Rewrite each logarithm as a quotient of natural logarithms. then, evaluate to the nearest hundredth. log(11)5 log(4)40

Conversion : yards to meters.1 yard = 0.9144 meters50 * 0.9144 = 45.72 mRay needs 45.72 meters of fishing line....

Rewrite each logarithm as a quotient of natural

lorenaandreahjimenez

14.01.2022

$\log_{11}(5)=0.671$ and $\log_4(40)=2.661$

Step-by-step explanation:

Given: $\log_{11}5$ and $\log_{4}40$

We have to rewrite each logarithm as a quotient of natural logarithms.

Using property of logarithm,

$\log_a(b)=\frac{\log_eb}{\log_ea}$

Consider 1) $\log_{11}5$

Applying property stated above,

$\log_{11}(5)=\frac{\log_e5}{\log_e11}$

We have ${\log_e5}=1.609$ (approx)

${\log_e11}=2.398$ (approx)

Substitute, we get,

$\log_{11}(5)=0.671$

Consider 2) $\log_{4}40$

Applying property stated above,

$\log_4(40)=\frac{\log_e40}{\log_e4}$

We have ${\log_e40}=3.689$ (approx)

${\log_e4}=1.386$ (approx)

Substitute, we get,

$\log_4(40)=2.661$

Thus, $\log_{11}(5)=0.671$ and $\log_4(40)=2.661$

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