Question

Log4 (4 7/17) - log4 (3 21/68) + log4 (48)

Answer 1

Log4 (4 7/17) - log4 (3 21/68) + log4 (48)=3

Answer 2

Using the logarithmic identity log a (b/c) = log a (b) - log a (c):

log4 (4 7/17) - log4 (3 21/68) + log4 (48)

= log4 [(4×17+7)/17] - log4 [(3×68+21)/68] + log4 (48)

= log4 (75/17) - log4 (213/68) + log4 (48)

Now, we can simplify the logarithms further by using the fact that log a (bc) = log a (b) + log a (c) and log a (b^c) = c log a (b):

= log4 (75) - log4 (17) - [log4 (213) - log4 (68)] + log4 (16×3)

= log4 (75) - log4 (17) - log4 (213) + log4 (68) + log4 (16) + log4 (3)

= log4 [(75×68×16)/(17×213×3)]

≈ log4 (4.23)

≈ 1.20 (rounded to two decimal places)

Therefore, log4 (4 7/17) - log4 (3 21/68) + log4 (48) ≈ 1.20.

Answer 3

This is not a true statement. From the solution above, we have:

log4 (4 7/17) - log4 (3 21/68) + log4 (48) ≈ 1.20

This means that the value of the expression is approximately equal to 1.20, not 3. There is no way to manipulate the logarithms to make the expression equal to 3.