Question

Log5 (75) - log5 (9) + log5 (15)

Answer 1

Ответ:

Пошаговое объяснение:

Всё подробно написала в решении.

Answer 2

To simplify the expression:

log5(75) - log5(9) + log5(15)

You can use logarithmic properties. Recall that:

1. log(a) - log(b) = log(a/b)
2. log(a) + log(b) = log(a * b)

Using these properties, we can simplify the expression step by step:

log5(75) - log5(9) + log5(15)

= log5(75/9) + log5(15)

Now, let's simplify 75/9:

75/9 = 25/3

So,

= log5(25/3) + log5(15)

Now, you can use the second property to combine the two logarithms:

= log5((25/3) * 15)

To further simplify, multiply 25/3 by 15:

(25/3) * 15 = 125/1 = 125

So,

= log5(125)

Now, you can express 125 as a power of 5:

125 = 5^3

So,

= log5(5^3)

Using the logarithm power rule (log_b(b^n) = n), we get:

= 3 * log5(5)

Now, log5(5) is equal to 1, so:

= 3 * 1

= 3

So, the simplified expression is 3.