Question

Log2 24+log2 12-log2 9

Answer 1

$\log_224+\log_212-\log_29 = \log_2(\frac{24\cdot12}{9}) =$

$= \log_2(8\cdot 4) = \log_232 = \log_22^5 = 5$

Answer 2

To solve this expression, we can use the properties of logarithms. Specifically, we can use the properties of addition, subtraction, and the logarithmic identity:

1. Logarithmic Identity: log_b(a) + log_b(c) = log_b(a * c)
2. Subtraction Property: log_b(a) - log_b(c) = log_b(a / c)

Given the expression:

log2(24) + log2(12) - log2(9)

We can apply the logarithmic identity to the first two terms:

log2(24 * 12) - log2(9)

Simplify the multiplication:

log2(288) - log2(9)

Now apply the subtraction property:

log2(288 / 9)

Simplify the division:

log2(32)

Since 2^5 = 32, we can rewrite the expression as:

log2(2^5)

And by the logarithmic identity, log_b(b) = 1:

1 * 5

So, the final result is:

5