Calculating log 54 base 10 and log 0.24 base 10
Logarithms are used to find the power to which a base must be raised to produce a given number. In this case, we are given the values of log 2 base 10 and log 3 base 10, which are 0.3010 and 0.4771 respectively. We can use these values to calculate the logarithms of other numbers.

Calculating log 54 base 10
To calculate log 54 base 10, we can use the properties of logarithms. We know that 54 can be expressed as 2 * 3^3. Therefore, we can rewrite log 54 base 10 as log (2 * 3^3) base 10.
Using the properties of logarithms, we can split this into log 2 base 10 + log (3^3) base 10. Since log 2 base 10 = 0.3010 and log 3 base 10 = 0.4771, we can substitute these values to get:
log 54 base 10 = log 2 base 10 + log (3^3) base 10
= 0.3010 + 3 * 0.4771
= 0.3010 + 1.4313
= 1.7323
Therefore, log 54 base 10 is equal to 1.7323.

Calculating log 0.24 base 10
To calculate log 0.24 base 10, we can express 0.24 as 2.4 * 10^-1. Therefore, log 0.24 base 10 can be rewritten as log (2.4 * 10^-1) base 10.
Using the properties of logarithms, we can split this into log 2.4 base 10 + log (10^-1) base 10. Since log 2.4 base 10 is not given directly, we can use log 2 base 10 = 0.3010 to approximate log 2.4 base 10.
log 2.4 base 10 ≈ log 2 base 10 + log 1.2 base 10
≈ 0.3010 + 0
≈ 0.3010
Therefore, log 0.24 base 10 is approximately equal to 0.3010 - 1 = -0.6990.