Question

Log1/5(30)-log1/5(6/5)

Answer 1

Решение на фото........

Answer 2

Упростить выражение,используя формулу log a(x)-log a(y)=logₐ( $\frac{x}{y}$):
log $\frac{1}{5}$ ( $\frac{\frac{30}{6}}{5}$);
Записать число в виде степени с основанием 5 и упростить составную дробь:
log₅⁻¹(25);
Записать число в виде степени с основанием 5:
log₅⁻¹(5²);
Упростить выражение,используя формулу logₐ^y(aˣ)= $\frac{x}{y}$:
-2

Answer 3

To simplify the expression, let's apply the properties of logarithms. The general rule we'll use is:

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

So, applying this rule to the given expression:

log₁/₅(30) - log₁/₅(6/5) = log₁/₅(30 / (6/5))

Now, to simplify further, we can convert the division into multiplication by the reciprocal:

log₁/₅(30 / (6/5)) = log₁/₅(30 * (5/6))

Now, we can simplify the expression inside the logarithm:

30 * (5/6) = 25

So, the expression becomes:

log₁/₅(25)

Now, let's find the value of this logarithm. Since 5^2 = 25, we can rewrite it as:

log₁/₅(25) = 2

Therefore, the simplified expression is 2.