Asked by Michael Bergamo on May 09, 2024
Verified
Solve the equation. Do not use a calculator. log68x=log648\log _ { 6 } 8 x = \log _ { 6 } 48log68x=log648
A) x=48x = 48x=48
B) x=6x = 6x=6
C) x=1x = 1x=1
D) x=8x = 8x=8
E) x=7x = 7x=7
Equation
A mathematical statement that asserts the equality of two expressions, usually involving variables and constants.
- Resolve equations that incorporate logarithms and recognize their value in mathematical settings.
Verified Answer
KJ
Kyl jane VasquezMay 12, 2024
Final Answer :
B
Explanation :
Using the fact that logb(bn)=n\log _ { b } ( b ^ { n } ) = nlogb(bn)=n , we can simplify the equation as follows: log68x=log648⇒log6(8x/48)=log6(1/6)\log _ { 6 } 8 x = \log _ { 6 } 48 \Rightarrow \log _ { 6 } (8x/48) = \log _ { 6 } (1/6)log68x=log648⇒log6(8x/48)=log6(1/6)
Now use the definition of logarithm logbc= ⟺ bd=c\log _ { b } c=\iff b^{d} = clogbc=⟺bd=c with base 6
6log6(8x/48)=6log6(1/6)⇒8x/48=1/66^{\log _ { 6 } (8x/48)} = 6^{\log _ { 6 } (1/6)} \Rightarrow 8x/48 = 1/66log6(8x/48)=6log6(1/6)⇒8x/48=1/6
Solving the above equation, we get x=6x=6x=6 . Therefore, the answer is B) x=6x = 6x=6 .
Now use the definition of logarithm logbc= ⟺ bd=c\log _ { b } c=\iff b^{d} = clogbc=⟺bd=c with base 6
6log6(8x/48)=6log6(1/6)⇒8x/48=1/66^{\log _ { 6 } (8x/48)} = 6^{\log _ { 6 } (1/6)} \Rightarrow 8x/48 = 1/66log6(8x/48)=6log6(1/6)⇒8x/48=1/6
Solving the above equation, we get x=6x=6x=6 . Therefore, the answer is B) x=6x = 6x=6 .
Learning Objectives
- Resolve equations that incorporate logarithms and recognize their value in mathematical settings.