Question $\log \frac{2}{5}=$ $\square$ $\ln 24.7=$

Studdy Solution

STEP 1

1. The problem involves evaluating logarithmic expressions.
2. We will use properties of logarithms to simplify and evaluate the expressions.

STEP 2

1. Evaluate $\log \frac{2}{5}$ .
2. Evaluate $\ln 24.7$ .

STEP 3

To evaluate $\log \frac{2}{5}$ , we can use the property of logarithms that states $\log \frac{a}{b} = \log a - \log b$ .
$\log \frac{2}{5} = \log 2 - \log 5$

STEP 4

To evaluate $\ln 24.7$ , we recognize that this is the natural logarithm of 24.7. This value is typically evaluated using a calculator, as it does not simplify neatly into a known logarithmic value.
$\ln 24.7 \approx 3.206$
The evaluated expressions are:
$\log \frac{2}{5} = \log 2 - \log 5$
$\ln 24.7 \approx 3.206$

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