How would I simplify this problem using logs? (25/16) -3/2

Is the -3/2 supposed to be an exponent? If so, precede it with a ^ symbol.

Hint: 25/16 = (5/4)^2

You should end up with 3 Log(4/5)

Wouldn't that be a decimal answer. Oh, and yes -3/2 is an exponent.

The answer, if turned into a number, will be a never-ending decimal. It's called an irrational number. I doubt if they want you to calculate it out to a lot of decimal places. You have also not specified the base of the logarithm. You'd have to do that to get a number

The base is 25/16.

To simplify the problem (25/16) - (3/2) using logs, we need to convert the equation to logarithmic form.

First, let's calculate the values of 25/16 and 3/2:

25/16 = 1.5625
3/2 = 1.5

Now, let's convert these values to logarithmic form. We'll use the common logarithm (log base 10):

log(1.5625) - log(1.5)

To simplify this, we can apply the logarithmic property which states that the difference between two logarithms with the same base is equal to the logarithm of the quotient of the two numbers:

log(1.5625/1.5)

Now, we can calculate the quotient:

1.5625/1.5 = 1.0416667

Plugging this value back into the equation, we get:

log(1.0416667)

To evaluate this logarithm, we can use either a scientific calculator or an online calculator:

log(1.0416667) ≈ 0.0178992

Therefore, the simplified result of (25/16) - (3/2) using logs is approximately 0.0178992.