What is the answer to 2log_{p}(9)+3log_{3}(p)=8 ?

The answer to 2log_{p}(9)+3log_{3}(p)=8 is p=9,p=3^{2/3}

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2log_{p}(9)+3log_{3}(p)=8

2 lo g_{p} (9) + 3 lo g_{3} (p) = 8

p = 9, p = 3^{\frac{2}{3}}

Solution steps

2 lo g_{p} (9) + 3 lo g_{3} (p) = 8

Apply log rules

\frac{4}{lo g _{3} ( p )} + 3 lo g_{3} (p) = 8

Rewrite the equation with

lo g_{3} (p) = u

\frac{4}{u} + 3 u = 8

Solve

\frac{4}{u} + 3 u = 8 : u = 2, u = \frac{2}{3}

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

Substitute back

u = lo g_{3} (p),

solve for

p

Solve

lo g_{3} (p) = 2 : p = 9

Solve

lo g_{3} (p) = \frac{2}{3} : p = 3^{\frac{2}{3}}

p = 9, p = 3^{\frac{2}{3}}

Verify Solutions:

p = 9

True

, p = 3^{\frac{2}{3}}

True

The solutions are

p = 9, p = 3^{\frac{2}{3}}

\frac{n}{lo g _{2} ( n )} = 8

2 lo g_{6} (x - 7) + lo g_{6} (9) = 2

lo g_{8} (x) = 0.333

2 lo g_{3} (x) - lo g_{27} (x) = 10

lo g_{125} (x) = - \frac{1}{3}

What is the answer to 2log_{p}(9)+3log_{3}(p)=8 ?
The answer to 2log_{p}(9)+3log_{3}(p)=8 is p=9,p=3^{2/3}
Solve for p: 2log_{p}(9)+3log_{3}(p)=8
The solution is p=9,p=3^{2/3}