Log1/4 x=-2 log3 x=3

To solve the equations provided, we need to convert the logarithmic equations into exponential form.

1. For the first equation: \[ \log_{1/4} x = -2 \] This means: \[ x = (1/4)^{-2} \] Calculating \( (1/4)^{-2} \): \[ (1/4)^{-2} = 4^2 = 16 \] So, \( x = 16 \).

2. For the second equation: \[ \log_{3} x = 3 \] This means: \[ x = 3^3 \] Calculating \( 3^3 \): \[ 3^3 = 27 \] So, \( x = 27 \).

Summary of Solutions:

• From the first equation: \( x = 16 \)
• From the second equation: \( x = 27 \)

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