Question

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

Answer 1

Answer:

Option 4 is correct that is $2^xlog5=log27$

Step-by-step explanation:

We have been given the expression:

$5\cdot 2^x=27$

Since, Gabriel used logarithms to solve the given equation

Taking log on both sides of the equation we get:

$log(5\cdot 2^x)=log(27)$

We will use the property of logarithmic function which is :

$logm^n=n\cdot logm$

Here, on left hand side of the equation

$m=5\text{and}n=2^x$ we get:

$2^xlog5=log27$

Hence, option 4 is correct.

Answer 2

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