Log²₅15-log²₅3+2log₅15+2log₅3 ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻ log₅15+log₅3

Предыдущий
вопрос Следующий
вопрос

To simplify this expression, we can use the properties of logarithms:

log₂₅15 - log₂₅3 + 2log₅15 + 2log₅3 - (log₅15 + log₅3)

First, let's simplify the terms with the same base:

= log₂₅(15/3) + 2log₅15 + 2log₅3 - (log₅(15*3))

= log₂₅5 + 2log₅15 + 2log₅3 - log₅45

Now, we can use the change of base formula for logs to simplify further:

= log5(5)/log5(25) + 2(log5(15)) + 2(log5(3)) - log5(45)

= 1/2 + 2log5(15) + 2log5(3) - log5(45)

Therefore, the simplified form of the given expression is 1/2 + 2log5(15) + 2log5(3) - log5(45).