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How do you solve #log x^2 =2#?

Answer 1

Madelyn Anderson

#x = +-10#

Assuming that's the common log, take the base 10 exponential of both sides, that is, the "sideth" power of 10.

#log(x^2) = 2# #x^2 = 10^2#

Take the root

#x = +-10#

Since #x^2# is positive for all values of #x# the only value of #x# we can't have is #0#, so both answers are okay.

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Answer 2

Elijah Allen

To solve the equation ( \log(x^2) = 2 ), you can use the properties of logarithms to simplify and solve for ( x ).

Start with the equation ( \log(x^2) = 2 ).
Apply the power rule of logarithms to bring down the exponent: ( 2\log(x) = 2 ).
Divide both sides by 2 to isolate ( \log(x) ): ( \log(x) = 1 ).
Rewrite the equation in exponential form: ( 10^1 = x ).
Simplify the right side to find the solution: ( x = 10 ).

Therefore, the solution to the equation ( \log(x^2) = 2 ) is ( x = 10 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.