Find the value of 1.57 - 0.42 leaving the answer as a mixed fraction in simplified form. 2. Oscar refuels his car every two days; Morris refuels his car after every four days while Millicent refuels h

Here are the solutions to the problems:

1. Find the value of $1.57 - 0.42$ leaving the answer as a mixed fraction in simplified form.

Step 1: Convert the decimals to fractions.

$$1.57 = \frac{157}{100}$$ $$0.42 = \frac{42}{100}$$

Step 2: Subtract the fractions.

$$\frac{157}{100} - \frac{42}{100} = \frac{157 - 42}{100} = \frac{115}{100}$$

Step 3: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 5.

$$\frac{115 \div 5}{100 \div 5} = \frac{23}{20}$$

Step 4: Convert the improper fraction to a mixed fraction.

$$\frac{23}{20} = 1 \frac{3}{20}$$

The value is $\boxed{1 \frac{3}{20}}$.

2. Oscar refuels his car every two days; Morris refuels his car after every four days while Millicent refuels her car after every ten days. If they all refueled their cars on $20^{th}$ March, on which date will they refuel their cars together again?

Step 1: Find the least common multiple (LCM) of 2, 4, and 10 to determine how many days it will be until they refuel together again.
Prime factorization:
$2 = 2^1$
$4 = 2^2$
$10 = 2^1 \times 5^1$
The LCM is $2^2 \times 5^1 = 4 \times 5 = 20$.
They will refuel together again after 20 days.

Step 2: Calculate the date 20 days after March 20th.
March has 31 days.
Days remaining in March from March 20th: $31 - 20 = 11$ days.
Remaining days to count in the next month: $20 - 11 = 9$ days.
The next month is April.
So, they will refuel together on April 9th.
The date is $\boxed{\text{April 9th}}$.

3. Use logarithms only to evaluate, correct to 4 decimal places:

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