Question

Log5(25)+log2(1/2)+lg10+lg1

Answer 1

$\displaystyle log_525+log_2\frac{1}{2}+lg10+lg1=log_55^2+log_22^{-1}+log_{10}10+log_{10}1=\\\\=2-1+1+0=2$

Answer 2

To solve this expression, let's break it down step by step:

1. Log5(25): This is asking for the logarithm of 25 with a base of 5. Since 5 raised to what power equals 25? The answer is 2. Therefore, log5(25) = 2.

2. Log2(1/2): This is asking for the logarithm of 1/2 with a base of 2. Since 2 raised to what power equals 1/2? The answer is -1. Therefore, log2(1/2) = -1.

3. lg10: This is asking for the logarithm of 10 with a base of 10. Since any number raised to the power of 1 equals itself, lg10 = 1.

4. lg1: This is asking for the logarithm of 1 with a base of 10. Since any number raised to the power of 0 equals 1, lg1 = 0.

Now, let's substitute the values back into the expression:

log5(25) + log2(1/2) + lg10 + lg1 = 2 + (-1) + 1 + 0 = 2 - 1 + 1 + 0 = 2 - 1 + 1 = 2 + 0 = 2

Therefore, the value of the expression log5(25) + log2(1/2) + lg10 + lg1 is 2.