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Gabriel is using logarithms to solve the equation 52x = 27. Which of the following equations would be equivalent to his original expression?
5 log 2x = log 27
2 log 5 = x log 27
x log 5 = 2 log 27
2x log 5 = log 27

Respuesta :

ghanami
Hello 
5^(2x) = 27
if : a>0  and b>0    a = b equivalent to  log(a) = log (b)
     log (5^(2x)) = log(27)  ... (1)
 a>0  and b>0  log(a^n) = nlog(a)
(1) equivalent to :2x log 5 = log 27

Answer:

Option 4 is correct that is [tex]2^xlog5=log27[/tex]

Step-by-step explanation:

We have been given the expression:

[tex]5\cdot 2^x=27[/tex]

Since, Gabriel used logarithms to solve the given equation

Taking log on both sides of the equation we get:

[tex]log(5\cdot 2^x)=log(27)[/tex]

We will use the property of logarithmic function which is :

[tex]logm^n=n\cdot logm[/tex]

Here, on left hand side of the equation

[tex]m=5\text{and}n=2^x[/tex] we get:

[tex]2^xlog5=log27[/tex]

Hence, option 4 is correct.


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