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Popular >

y=ln(5x)*ln(6x)

Solution

y = ln (5 x) \cdot ln (6 x)

Solution

Domain : x > 0

Range : f (x) \geq - \frac{ln ^{2} ( 30 )}{4} + ln (5) ln (6)

X Intercepts : (\frac{1}{5}, 0), (\frac{1}{6}, 0)

Asymptotes : Vertical x = 0

Extreme Points : Minimum (\frac{1}{30}, \frac{1}{4} ln (\frac{5}{6}) ln (\frac{6}{5}))

+1

Solution steps

Domain of

ln (5 x) \cdot ln (6 x) : x > 0

Range of

ln (5 x) \cdot ln (6 x) : f (x) \geq - \frac{ln ^{2} ( 30 )}{4} + ln (5) ln (6)

Axis interception points of

ln (5 x) \cdot ln (6 x) :

X Intercepts

: (\frac{1}{5}, 0), (\frac{1}{6}, 0)

Asymptotes of

ln (5 x) \cdot ln (6 x) :

Vertical

: x = 0

Extreme Points of

ln (5 x) \cdot ln (6 x) :

Minimum

(\frac{1}{30}, \frac{1}{4} ln (\frac{5}{6}) ln (\frac{6}{5}))

Popular Examples

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f (x) = 11 x + 15 x^{2} - sin (6 x)

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f (x) = x^{4} - 6 x^{3} + x^{2} + 24 x - 20

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y=3e^{2x}+e^{-2x}-3x

y = 3 e^{2 x} + e^{- 2 x} - 3 x

y = x + \frac{1}{2 x}

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