# let log2=a, log3=b, and log5=c. express the indicated logarithm in terms of a, b, and c.

log6/25

log 100

## log 6/25= log (3*2)/(5^2)

= log 3 + log2 - 2 log5

## Well, let's put our clown noses on and have some fun with logarithms!

For the first one, we want to express log(6/25) in terms of a, b, and c.

First, let's simplify 6/25. That's like trying to divide a pie into 6 pieces and only keeping two of them. So, 6/25 is just 2/5.

Now, we can rewrite log(6/25) as log(2/5).

Since we know that log(2/5) is log(2) - log(5), and we're given that log(2) = a and log(5) = c, we can substitute those values in.

Therefore, log(6/25) = a - c.

For the second one, we want to express log(100) in terms of a, b, and c.

Well, 100 is a perfect square, and it can be written as 10^2.

So, log(100) is the same as log(10^2).

Using the logarithmic property log(x^y) = y log(x), we get 2 log(10).

But, log(10) is simply log(2) + log(5), which is a + c.

So, log(100) = 2(a + c).

I hope that brought a smile to your face!

## To express the logarithm in terms of a, b, and c, we can use the properties of logarithms.

1. log6/25:

We can use the property that log a/b = log a - log b to rewrite log6/25 as log(6) - log(25). Since we are given the values of log2 (a), log3 (b), and log5 (c), we can substitute these values into the expression:

log6/25 = log(2*3) - log(5*5) = log(2) + log(3) - log(5) - log(5) = a + b - c - c = a + b - 2c

2. log100:

We know that 100 can be expressed as 10^2. And we know that log a^b = b * log a. So we can rewrite log100 as 2 * log10. Since we are given the values of log2 (a), log3 (b), and log5 (c), we can substitute these values into the expression:

log100 = 2 * log10 = 2 * log(2*5) = 2 * (log(2) + log(5)) = 2 * (a + c) = 2a + 2c

Therefore, log6/25 can be expressed as a + b - 2c, and log100 can be expressed as 2a + 2c.

## log 100

= log(25*4)

= log 25 + log 4

= log 5^2 + log 2^2

= 2log5 + 2log2

= 2c + 2a