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2 votes
Solve 2 log x = log 64.
x= 1.8
x=8
x= 32
x=128

User TetonSig
by
7.9k points

2 Answers

0 votes

Answer:

x = 8

Explanation:

Given expression:


2\log x=\log 64


\textsf{Apply the log power law}: \quad n\log x=\log x^n


\implies \log x^2=\log 64

Rewrite 64 as 8²:


\implies \log x^2=\log 8^2


\textsf{Apply the log equality law}: \quad \textsf{If\;\;$\log x=\log y$\;\;then\;\;$x=y$}


\implies x^2=8^2

Square root both sides:


\implies x=8

User Maninda
by
7.7k points
6 votes

Answer:

x=8.

Explanation:

1. Write the expression.


2log(x)=log(64)

2. Divide both sides of the equation by "2".


(2log(x))/(2) =(log(64))/(2)\\ \\log(x)=(log(64))/(2)

3. Apply number "10" as the base of an exponent of each side of the equation.

When a logarithm doesn't have it's base expressed (base is tipically written as a subscript) we can assume it'sbase is 10. Therefore, to solve this equation, take the following step:


10^(log(x)) =10^{(log(64))/(2)} \\ \\x=10^{(log(64))/(2)}\\ \\x=8

4. Verify the answer.

If the result is correct, then the equation should return the same value of both sides of the equal symbol (=) when we substitute the variable "x" by it's calculated value, 8.


2log(8)=log(64)\\ \\1.806179974=1.806179974

As you can tell, the same number appears on both sides of the equal symbol, this means that the result is correct!

User Vinu Prasad
by
6.9k points