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kittendude
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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

Verified Answer :

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 \(2^xlog5=log27\)

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.


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