What is the answer to log_{y}(2)=log_{4}(32) ?

The answer to log_{y}(2)=log_{4}(32) is y=2^{2/5}

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log_{y}(2)=log_{4}(32)

lo g_{y} (2) = lo g_{4} (32)

y = 2^{\frac{2}{5}}

Decimal Notation

y = 1.31950 \dots

Solution steps

lo g_{y} (2) = lo g_{4} (32)

Apply log rules

\frac{1}{lo g _{2} ( y )} = \frac{5}{2}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

1 \cdot 2 = lo g_{2} (y) \cdot 5

Simplify

2 = lo g_{2} (y) \cdot 5

Switch sides

lo g_{2} (y) \cdot 5 = 2

Divide both sides by

5

lo g_{2} (y) = \frac{2}{5}

Apply log rules

y = 2^{\frac{2}{5}}

Verify Solutions:

y = 2^{\frac{2}{5}}

True

The solution is

y = 2^{\frac{2}{5}}

ln^{2} (x) - ln (x) = 0

ln (5 x - 15) = 1

3 lo g_{4} (x) = lo g_{4} (4^{8}) - 5

x, lo g_{k} (x) = - 4

lo g_{\frac{1}{7}} (x) = 2

What is the answer to log_{y}(2)=log_{4}(32) ?
The answer to log_{y}(2)=log_{4}(32) is y=2^{2/5}
Solve for y: log_{y}(2)=log_{4}(32)
The solution is y=2^{2/5}