Question

Log(12)6=a, log(12)11=b. Найдите log(24)132

Answer 1

Решение задания приложено

Answer 2

To find the value of log base 24 of 132, we can use the properties of logarithms to express it in terms of the given logarithms.

First, recall the change of base formula for logarithms:

log_a(b) = log_c(b) / log_c(a)

where log_a(b) represents the logarithm of b with base a and log_c(x) is the logarithm of x with base c.

Now, let's find log base 24 of 132:

log(24)132 = log(12 * 2)132 [since 24 = 12 * 2]

Using the properties of logarithms:

log(12 * 2)132 = log(12)132 / log(12)24

Now, we can express log(12)132 in terms of a and log(12)24 in terms of b:

log(12)132 = log(12) (6 * 22) [since 132 = 6 * 22] = log(12)6 + log(12)2

And similarly:

log(12)24 = log(12) (6 * 2) [since 24 = 6 * 2] = log(12)6 + log(12)2

Now, using the given information:

log(12)6 = a log(12)2 = log(12)(2) = log(12)(2^1) = 1 * log(12)(2) = b

Now we can substitute these values back into the expression:

log(12)132 = (a + b) / b

Finally, let's express log(12)132 in terms of log(12)11 (b):

log(12)11 = b

Thus, the final expression for log(12)132 is:

log(12)132 = (a + log(12)11) / log(12)11

Now, if you have the values of a and b (the values of log(12)6 and log(12)11), you can plug them into this formula to calculate log(12)132.