What is the answer to log_{3}(y+14)=(1+2)/((log_{y)(3))} ?

The answer to log_{3}(y+14)=(1+2)/((log_{y)(3))} is y\approx 2.54830…

Solve for y: log_{3}(y+14)=(1+2)/((log_{y)(3))}

The solution is y\approx 2.54830…

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lo g_{3} (y + 14) = \frac{1 + 2}{( lo g _{y} ( 3 ) )}

y \approx 2.54830 \dots

Solution steps

lo g_{3} (y + 14) = \frac{1 + 2}{( lo g _{y} ( 3 ) )}

Simplify

\frac{1 + 2}{lo g _{y} ( 3 )} : \frac{3}{lo g _{y} ( 3 )}

lo g_{3} (y + 14) = \frac{3}{lo g _{y} ( 3 )}

Multiply both sides by

lo g_{y} (3)

\frac{ln ( y + 14 )}{ln ( y )} = 3

Multiply both sides by

ln (y)

ln (y + 14) = 3 ln (y)

Solve

ln (y + 14) = 3 ln (y) : y \approx 2.54830 \dots

y \approx 2.54830 \dots

Verify Solutions

Find undefined (singularity) points:

y = - 14, y = 0, y = 1

Combine undefined points with solutions:

y \approx 2.54830 \dots

2 (x - [\frac{1}{x}])^{2} + 3 (x + [\frac{1}{x}]) - 12 = 0

\frac{1}{( x + 2 )} + \frac{1}{x} = \frac{3}{4}

\frac{3.5}{x} = \frac{10.5}{6}

x \cdot x^{- 3} = \frac{27}{64}

(x + 2) \cdot (\frac{100}{x - 15}) = 100

What is the answer to log_{3}(y+14)=(1+2)/((log_{y)(3))} ?
The answer to log_{3}(y+14)=(1+2)/((log_{y)(3))} is y\approx 2.54830…
Solve for y: log_{3}(y+14)=(1+2)/((log_{y)(3))}
The solution is y\approx 2.54830…