Asked by Milanpreet kaur Chana on May 12, 2024
Verified
Determine whether the value x=3438x = \frac { 343 } { 8 }x=8343 is a solution of the equation log49(8x) =32\log _ { 49 } ( 8 x ) = \frac { 3 } { 2 }log49(8x) =23 .
A) solution
B) not a solution
Solution
The value or set of values that satisfy an equation, inequality, or system of equations, providing the answer to a mathematical problem.
Equation
A mathematical statement that asserts the equality of two expressions, typically in the form of 'A = B' where A and B can be algebraic expressions.
Logarithm
The exponent or power to which a base must be raised to yield a given number, generally expressed as log_base(number).
- Employ logarithmic principles to decipher equations.
Verified Answer
SC
Sienisha CooperMay 12, 2024
Final Answer :
A
Explanation :
Substituting x=3438x=\frac{343}{8}x=8343 into the equation yields:
log49(8⋅3438)=log49(343)=32\begin{align*}\log_{49}\left(8\cdot\frac{343}{8}\right)&=\log_{49}(343)\\&=\frac{3}{2}\end{align*}log49(8⋅8343)=log49(343)=23
Since the left-hand side and right-hand side are equal, we have shown that x=3438x=\frac{343}{8}x=8343 is a solution to the equation. Thus, the answer is (A).
log49(8⋅3438)=log49(343)=32\begin{align*}\log_{49}\left(8\cdot\frac{343}{8}\right)&=\log_{49}(343)\\&=\frac{3}{2}\end{align*}log49(8⋅8343)=log49(343)=23
Since the left-hand side and right-hand side are equal, we have shown that x=3438x=\frac{343}{8}x=8343 is a solution to the equation. Thus, the answer is (A).
Learning Objectives
- Employ logarithmic principles to decipher equations.