Question

Log₆15+log₆10-log₆(15+10)= log₂32+log₃7log₇3=

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To solve the given logarithmic expressions, let's break them down step by step:

1. Log₆15 + log₆10 - log₆(15 + 10):

Using logarithmic properties, we can rewrite this expression as a single logarithm:

= log₆(15 * 10) - log₆(25)

= log₆(150) - log₆(25)

Now, we can simplify further by applying the logarithmic subtraction rule:

= log₆(150/25)

= log₆(6)

The expression simplifies to log₆(6).

2. Log₂32 + log₃7log₇3:

First, let's simplify log₃7log₇3. This can be done by using the logarithmic change of base formula:

log₃7log₇3 = (log₇3) / (log₇7)

Since log₇7 is equal to 1, we can simplify further:

log₃7log₇3 = log₇3

Now, let's substitute this back into the original expression:

= log₂32 + log₇3

Since 32 can be expressed as 2^5, we have:

= log₂(2^5) + log₇3

Applying the logarithmic property, we can rewrite log₂(2^5) as 5:

= 5 + log₇3

The expression simplifies to 5 + log₇3.