Question

Зная, что a^2=b, найдите log числа b по основанию a

Answer 1

a²=b;

$log_ab=2;$

Answer 2

To find the logarithm of a number b with base a, you can use the logarithmic identity:

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

where log_a(b) represents the logarithm of b with base a, and log_c() is the logarithm to any base c. In this case, we will use the natural logarithm (base e), but you can use any logarithm as long as you are consistent.

So, given that a^2 = b, we can take the natural logarithm of both sides:

ln(a^2) = ln(b)

Now, using the property of logarithms, we can bring down the exponent:

2 * ln(a) = ln(b)

Finally, to find the logarithm of b with base a, divide both sides by 2 * ln(a):

log_a(b) = ln(b) / (2 * ln(a))

That's the solution for the logarithm of b with base a in terms of natural logarithms.