Question

Log¼8 - log¼3 +log¼24

Answer 1

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Answer 2

To solve this expression, we can use the properties of logarithms. Let's first rewrite the expression using the properties of logarithms:

log¼(8) - log¼(3) + log¼(24)

Now, we know that the property of subtraction of logarithms states that:

logᵦ(x) - logᵦ(y) = logᵦ(x/y)

Applying this property to our expression:

log¼(8/3) + log¼(24)

Now, let's simplify further:

log¼(8/3) can be written as log₄(8/3) since the base ¼ is equivalent to the base 4.

Similarly, log¼(24) is log₄(24).

Now, the expression becomes:

log₄(8/3) + log₄(24)

According to the property of addition of logarithms:

logₐ(x) + logₐ(y) = logₐ(xy)

We can apply this property to our expression:

log₄(8/3 * 24)

Now, let's simplify the inside of the logarithm:

8/3 * 24 = 64

The expression becomes:

log₄(64)

Finally, we need to determine what exponent we need to raise 4 to in order to get 64:

4^3 = 64

So, log₄(64) = 3

Therefore, the final answer is 3.