Solve using logarithms: [tex]5^{(3x-6)} = 125[/tex]

Question

facundo3141592 · Answer

The solution of the exponential equation is x = 3. 
 How to solve the exponential equation? 
 Here we want to solve the equation: 
 5 3 x − 6 = 125 
 To solve it we need to apply the natural logarithm in both sides of the equation: 
 l n ( 5 3 x − 6 ) = l n ( 125 ) ( 3 x − 6 ) ∗ l n ( 5 ) = l n ( 125 ) ( 3 x − 6 ) = l n ( 125 ) / l n ( 5 ) = 3 
 Now we just need to solve a line: 
 3x - 6 = 3 
 3x = 3 +6 
 x = 9/3 
 x = 3

facundo3141592 · Answer

To solve 5 ( 3 x − 6 ) = 125 , rewrite 125 as 5 3 and set the exponents equal. Solving for x , we find x = 3 . 
 ;

Solve using logarithms: [tex]5^{(3x-6)} = 125[/tex]

Answer (2)

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