Question

which equation(s) have ( x = 2 ) as the solution? choose two correct answers.
( log_{3}(6x + 4) = 3 )
( log_{x} 36 = 6 )
( log_{2}(5x + 6) = 4 )
( log_{x} 16 = 4 )

Explanation:

Step1: Test $x=2$ in first equation

Substitute $x=2$ into $\log_{3}(6x+4)$:
$\log_{3}(6\times2 + 4)=\log_{3}(16)\approx2.52
eq3$

Step2: Test $x=2$ in second equation

Substitute $x=2$ into $\log_{x}36$:
$\log_{2}36=\frac{\ln36}{\ln2}\approx5.17
eq6$

Step3: Test $x=2$ in third equation

Substitute $x=2$ into $\log_{2}(5x+6)$:
$\log_{2}(5\times2 + 6)=\log_{2}(16)=4$

Step4: Test $x=2$ in fourth equation

Substitute $x=2$ into $\log_{x}16$:
$\log_{2}16=4$

Answer:

$\log_{2}(5x + 6) = 4$, $\log_{x}16 = 4$