Question

Log2 18+log2 25/9+log2 1/25

Answer 1

Ответ:

Объяснение:

           

log₂ (18*(25/9)*1/25)=log₂2=1

Answer 2

To solve the expression log2(18) + log2(25/9) + log2(1/25), you can use the properties of logarithms. The key properties to remember are:

1. log_a(b) + log_a(c) = log_a(b * c)
2. log_a(b) - log_a(c) = log_a(b / c)

Using these properties, let's simplify the expression step by step:

log2(18) + log2(25/9) + log2(1/25)

First, apply property 1 to the first two terms:

log2(18 * (25/9)) + log2(1/25)

Now, simplify the product inside the first logarithm:

log2((18 * 25) / 9) + log2(1/25)

Next, simplify the fraction inside the first logarithm:

log2((450/9) + log2(1/25)

Now, simplify the fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 9:

log2(50) + log2(1/25)

Now, apply property 1 to the two logarithms:

log2(50 * (1/25))

Now, simplify the product inside the logarithm:

log2(50 / 25)

Finally, simplify the fraction inside the logarithm:

log2(2)

Since log2(2) = 1, the final answer is:

1