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If log 4 16 = log x 36, find x.

User EPascoal
by
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1 Answer

2 votes

Answer:

x = 6

Explanation:

Given the logarithmic equation:


\displaystyle{\log_4 16 = \log_x 36}

The left side can be simplified to 2 because:


\displaystyle{\log_4 16 = x}\\\\\displaystyle{4^x = 16}

And we know that if x = 2 then it'd be true for the equation: So the left side is simplified to 2:


\displaystyle{2 = \log_x 36}

Convert logarithm to exponential where:


\displaystyle{\log_a b = n \to a^n = b}

Apply the property:


\displaystyle{\log_x 36 = 2 \to x^2 = 36}\\\\\displaystyle{x^2=36}

Solve the quadratic equation for x, square root both sides:


\displaystyle{√(x^2)=√(36)

Cancel square and add plus-minus to right side:


\displaystyle{x=\pm √(36)}\\\\\displaystyle{x=\pm 6}

However, for logarithm function, it's defined that the base cannot be negative. Therefore, -6 is an extraneous solution while x = 6 is the only valid solution.

Therefore, x = 6.

User Bornytm
by
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