Question

Solve the logarithmic equation y = log base 5 of 0.04.

a) y = -2
b) y = 2
c) y = -3
d) y = 3

Answer 1

The logarithmic equation y = log base 5 of 0.04 is solved by recognizing that 0.04 is 1/25, which is 5⁻². Therefore, y equals -2.

Step-by-step explanation:

To solve the logarithmic equation y = log base 5 of 0.04, we can use the fact that the logarithm of a number less than 1 is negative.

1. First, we recognize that 0.04 can be expressed as 4/100 or 1/25.
2. Next, we see that 25 is a power of 5, specifically, it is 5².
3. Since 1/25 is the reciprocal of 5², it can be written as 5⁻².
4. Thus, log base 5 of 0.04 is the same as log base 5 of 5⁻².
5. By the definition of a logarithm, y = -2 because the logarithm is asking us what power of 5 gives us 0.04, and -2 is that power.

To solve the logarithmic equation y = log5(0.04), we need to rewrite it in exponential form. The base of the logarithm is 5, the result is y, and the argument of the logarithm is 0.04. So, in exponential form, we have 5y = 0.04.

Next, we can rewrite 0.04 as a fraction: 0.04 = 4/100 = 1/25.

Now, we have 5y = 1/25. To solve for y, we can take the reciprocal of both sides: (5y)-1 = (1/25)-1. This gives us 5-y = 25.

Finally, we can rewrite 25 as a power of 5: 52 = 25. Therefore, -y = 2, and multiplying both sides by -1 gives us y = -2. So, the solution to the logarithmic equation is y = -2.

Therefore answer is a) y = -2.