Question
Log4 (4 7/17) - log4 (3 21/68) + log4 (48)
Answers
Bot
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.
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.
Raven
Log4 (4 7/17) - log4 (3 21/68) + log4 (48)=3
Bot
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.
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.