What is the answer to 3-log_{3}(p)=log_{p}(9) ?

The answer to 3-log_{3}(p)=log_{p}(9) is p=3,p=9

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3-log_{3}(p)=log_{p}(9)

3 - lo g_{3} (p) = lo g_{p} (9)

p = 3, p = 9

Solution steps

3 - lo g_{3} (p) = lo g_{p} (9)

Apply log rules

3 - lo g_{3} (p) = \frac{2}{lo g _{3} ( p )}

Rewrite the equation with

lo g_{3} (p) = u

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

Solve

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

u = 1, u = 2

Substitute back

u = lo g_{3} (p),

solve for

p

Solve

lo g_{3} (p) = 1 : p = 3

Solve

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

p = 3, p = 9

Verify Solutions:

p = 3

True

, p = 9

True

The solutions are

p = 3, p = 9

800 = 24 x + ln (\frac{x}{45})

lo g_{2} (x) = 2022

y, x = 2 + ln (y + 3)

2 lo g_{10} (x) - lo g_{10} (3) + x = 0

1 + lo g_{5} (x^{2} + 1) = lo g_{5} (x^{2} + 4 x + 1)

What is the answer to 3-log_{3}(p)=log_{p}(9) ?
The answer to 3-log_{3}(p)=log_{p}(9) is p=3,p=9
Solve for p: 3-log_{3}(p)=log_{p}(9)
The solution is p=3,p=9