Question

Крайне срочно!!!!!!! Лог основание 5 75 + лог 5 (25) в степени минус 1

Answer 1

Log 5 75 + log 5 (25)-1 = log 5 (75*(25)-1) = log 5 (75/25) = log 5 3

Answer 2

Calculation of log base 5 of 75 and log base 5 of (25) to the power of -1

To calculate the logarithm of a number, we need to know the base of the logarithm. In this case, the base is 5.

The logarithm of 75 to the base 5 can be calculated as follows:

log base 5 of 75

Using the logarithmic identity, we can express 75 as a power of 5:

75 = 5^2 * 3

Therefore, we can rewrite the expression as:

log base 5 of 75 = log base 5 of (5^2 * 3)

Using the logarithmic property that log base b of (a * c) = log base b of a + log base b of c, we can split the expression:

log base 5 of 75 = log base 5 of 5^2 + log base 5 of 3

Since log base b of b^x = x, we can simplify further:

log base 5 of 75 = 2 + log base 5 of 3

Now, let's calculate the logarithm of 3 to the base 5:

log base 5 of 3

To find the logarithm of 3 to the base 5, we need to determine what power of 5 equals 3.

Since 5^1 = 5 and 5^2 = 25, we know that the logarithm of 3 to the base 5 is between 1 and 2.

To find a more precise value, we can use interpolation or approximation methods. However, without additional information, we cannot determine the exact value of log base 5 of 3.

Finally, let's calculate the logarithm of (25) to the power of -1:

log base 5 of (25) to the power of -1

Using the logarithmic property that log base b of (a^x) = x * log base b of a, we can rewrite the expression as:

log base 5 of (25) to the power of -1 = -1 * log base 5 of 25

Since 25 = 5^2, we can simplify further:

log base 5 of (25) to the power of -1 = -1 * 2

Therefore, the logarithm of (25) to the power of -1 to the base 5 is -2.

Please note that the exact values of log base 5 of 3 and log base 5 of (25) to the power of -1 cannot be determined without additional information. The calculations provided above are based on the given information and mathematical principles.