match each logarithmic equation with its solution.\n2 log₅ 2x = 12\nlog₅ x + 3 = 6\nlog₅ 2x = 3\n3 log₅ x =…
match each logarithmic equation with its solution.\n2 log₅ 2x = 12\nlog₅ x + 3 = 6\nlog₅ 2x = 3\n3 log₅ x = 15\n62.5\n7,812.5\n3,125\n125
Answer
Explanation:
Step1: Solve $2\log_5{2x}=12$
Divide both sides by 2: $\log_5{2x} = 6$. By the definition of logarithms, $2x=5^6$, so $x=\frac{5^6}{2}=\frac{15625}{2}=7812.5$.
Step2: Solve $\log_5{x}+3 = 6$
Subtract 3 from both sides: $\log_5{x}=3$. By the definition of logarithms, $x = 5^3=125$.
Step3: Solve $\log_5{2x}=3$
By the definition of logarithms, $2x = 5^3$, so $x=\frac{5^3}{2}=\frac{125}{2}=62.5$.
Step4: Solve $3\log_5{x}=15$
Divide both sides by 3: $\log_5{x}=5$. By the definition of logarithms, $x = 5^5=3125$.
Answer:
$2\log_5{2x}=12$ - $7812.5$ $\log_5{x}+3 = 6$ - $125$ $\log_5{2x}=3$ - $62.5$ $3\log_5{x}=15$ - $3125$