Question

Log(14)7=a, log(14)5=b. Найдите log(28)35

Answer 1

$log_{28}35= \frac{log_{14}35}{log_{14}28} = \frac{log_{14}(7*5)}{log_{14}(14*2)} = \\ \\ = \frac{log_{14}7+log_{14}5}{log_{14}14+log_{14}2} = \frac{a+b}{1+ log_{14}(14/7)} = \\ \\ = \frac{a+b}{1+log_{14}14-log_{14}7} = \frac{a+b}{1+1-a} = \frac{a+b}{2-a}$

Answer 2

To find the value of log(28)35 using the given information, we can use the properties of logarithms. Specifically, we'll use the change of base formula, which states:

log(base a) b = log(base c) b / log(base c) a

where "c" can be any base we choose.

Given: log(14)7 = a log(14)5 = b

Now, let's express log(28)35 in terms of a and b:

log(28)35 = log(14 * 2)35

We can split the logarithm using the properties of logarithms:

log(28)35 = log(14)35 + log(2)35

Now, let's use the change of base formula for each term:

log(14)35 = log(35) / log(14) log(2)35 = log(35) / log(2)

Therefore, we get:

log(28)35 = (log(35) / log(14)) + (log(35) / log(2))

Now, substitute the given values:

log(28)35 = (log(35) / a) + (log(35) / b)

Now, since log(35) is common in both terms, we can factor it out:

log(28)35 = log(35) * (1/a + 1/b)

Finally, substitute the given values of a and b:

log(28)35 = log(35) * (1/log(14) + 1/log(14))

Now, simplify the expression:

log(28)35 = log(35) * (2 / log(14))

So, the value of log(28)35 in terms of a and b is:

log(28)35 = 2 * (log(35) / log(14))

You can calculate the approximate value using a calculator if needed.