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

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 2

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

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.