How do you simplify \log _ { 2} ( \frac { x ^ { 6} y ^ { 7} } { 8} )log2(x6y78)?
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∙loga(nm)=logan+logam
•log_a(n/m) = log_an - log_a m∙loga(nm)=logan−logam
•log(a^n) = nloga∙log(an)=nloga
Now apply them:
=log_2(x^6y^7) - log_2 8=log2(x6y7)−log28
= log_2 x^6 + log_2 y^7 - 3=log2x6+log2y7−3
=6log_2x + 7log_2y - 3=6log2x+7log2y−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