How do you simplify \log _ { 2} ( \frac { x ^ { 6} y ^ { 7} } { 8} )?
2 Answers
The expression equals
Explanation:
Use the following laws of logarithms to simplify the above problem
• log_a(nm) = log_a n + log_a m
•log_a(n/m) = log_an - log_a m
•log(a^n) = nloga
Now apply them:
=log_2(x^6y^7) - log_2 8
= log_2 x^6 + log_2 y^7 - 3
=6log_2x + 7log_2y - 3
Hopefully this helps!
Explanation:
Use log properties:
Product Rule:
Quotient Rule:
Split the fraction into two separate logs using the Quotient Rule.
Split
Simplify