Question

Log0,36 5 - log0,36 3

Answer 1

$\displaystyle \log_{0.36}5-\log_{0.36}3=-\log_{0.36} \frac{3}{5} =-\log_{0.6^2}0.6=-0.5\log_{0.6}0.6=-0.5$

Answer 2

To calculate this expression, we'll first use the property of logarithms that states:

log_b(a) - log_b(c) = log_b(a/c)

So, in this case:

log_0.36(5) - log_0.36(3) = log_0.36(5/3)

Now, we need to find the value of log_0.36(5/3). To do that, we need to find what exponent (let's call it x) we must raise 0.36 to in order to get 5/3:

0.36^x = 5/3

Now, we can solve for x:

x = log_0.36(5/3)

Using the change of base formula, we can convert this to a logarithm with base 10:

x = log(5/3) / log(0.36)

Using a calculator:

x ≈ 0.5265

Therefore, log_0.36(5) - log_0.36(3) ≈ 0.5265.