Question

Lg 1/5 + log100 25 Найти значение выражения

Answer 1

Lg 1/5 + log₁₀₀ 25 = lg1 - lg5 + lg25/lg100 = -lg5 +2lg5/2 = -lg5 +lg5 = 0

Answer 2

To find the value of the expression "lg(1/5) + log100(25)," let's first simplify each term individually:

1. lg(1/5): lg represents the base-10 logarithm. The expression lg(1/5) means "the logarithm of 1/5 with base 10." Since 10^x = 1/5, we need to find the value of x:

10^x = 1/5

Now, we know that 1/5 is the same as 5^(-1), so we can rewrite the equation as:

10^x = 5^(-1)

Now, we take the logarithm of both sides using the same base, which is 10:

lg(10^x) = lg(5^(-1))

The log of the exponent cancels out the base, and we get:

x = -1

So, lg(1/5) = -1.

2. log100(25): log100 represents the base-100 logarithm. The expression log100(25) means "the logarithm of 25 with base 100." Since 100^x = 25, we need to find the value of x:

100^x = 25

Now, we know that 25 is the same as 5^2, so we can rewrite the equation as:

100^x = 5^2

Now, we take the logarithm of both sides using the same base, which is 100:

log100(100^x) = log100(5^2)

The log of the exponent cancels out the base, and we get:

x = 2

So, log100(25) = 2.

Now, we can find the value of the whole expression:

lg(1/5) + log100(25) = -1 + 2 = 1

The value of the expression is 1.