What is the answer to 2*log_{2}(y)+3*log_{y}(2)=7 ?

The answer to 2*log_{2}(y)+3*log_{y}(2)=7 is y=8,y=sqrt(2)

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Popular >

2log_{2}(y)+3log_{y}(2)=7

Solution

2 \cdot lo g_{2} (y) + 3 \cdot lo g_{y} (2) = 7

Solution

y = 8, y = 2

Decimal Notation

y = 8, y = 1.41421 \dots

Solution steps

2 lo g_{2} (y) + 3 lo g_{y} (2) = 7

Apply log rules

2 lo g_{2} (y) + \frac{3}{lo g _{2} ( y )} = 7

Rewrite the equation with

lo g_{2} (y) = u

2 u + \frac{3}{u} = 7

Solve

2 u + \frac{3}{u} = 7 : u = 3, u = \frac{1}{2}

u = 3, u = \frac{1}{2}

Substitute back

u = lo g_{2} (y),

solve for

y

Solve

lo g_{2} (y) = 3 : y = 8

Solve

lo g_{2} (y) = \frac{1}{2} : y = 2

y = 8, y = 2

Verify Solutions:

y = 8

True

, y = 2

True

The solutions are

y = 8, y = 2

Popular Examples

log_{2}(x-3)=3

lo g_{2} (x - 3) = 3

log_{3}(3x-2)=2

lo g_{3} (3 x - 2) = 2

log_{2}(x+3)-2log_{2}(x)=4

lo g_{2} (x + 3) - 2 lo g_{2} (x) = 4

ln(p^2)=ln(10p)-3

ln (p^{2}) = ln (10 p) - 3

x/(log_{10)(x)(1/32)}=5

\frac{x}{lo g _{10} ( x ) ( \frac{1}{32} )} = 5

Frequently Asked Questions (FAQ)

What is the answer to 2*log_{2}(y)+3*log_{y}(2)=7 ?
The answer to 2*log_{2}(y)+3*log_{y}(2)=7 is y=8,y=sqrt(2)
Solve for y: 2*log_{2}(y)+3*log_{y}(2)=7
The solution is y=8,y=sqrt(2)

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to 2log_{2}(y)+3log_{y}(2)=7 ?

Solve for y: 2log_{2}(y)+3log_{y}(2)=7

2*log_{2}(y)+3*log_{y}(2)=7

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to 2*log_{2}(y)+3*log_{y}(2)=7 ?

Solve for y: 2*log_{2}(y)+3*log_{y}(2)=7

2log_{2}(y)+3log_{y}(2)=7

What is the answer to 2log_{2}(y)+3log_{y}(2)=7 ?

Solve for y: 2log_{2}(y)+3log_{y}(2)=7