What are the solutions to the equation log_{10}(9)(2n^2-14n)=log_{10}(9)(-45+n^2) ?

The solutions to the equation log_{10}(9)(2n^2-14n)=log_{10}(9)(-45+n^2) are n=5,n=9

Find the zeros of log_{10}(9)(2n^2-14n)=log_{10}(9)(-45+n^2)

The zeros of log_{10}(9)(2n^2-14n)=log_{10}(9)(-45+n^2) are n=5,n=9

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lo g_{10} (9) (2 n^{2} - 14 n) = lo g_{10} (9) (- 45 + n^{2})

n = 5, n = 9

Solution steps

lo g_{10} (9) (2 n^{2} - 14 n) = lo g_{10} (9) (- 45 + n^{2})

Move

lo g_{10} (9) (- 45 + n^{2})

to the left side

lo g_{10} (9) (2 n^{2} - 14 n) - lo g_{10} (9) (- 45 + n^{2}) = 0

Factor

lo g_{10} (9) (2 n^{2} - 14 n) - lo g_{10} (9) (- 45 + n^{2}) : 2 lo g_{10} (3) (n - 5) (n - 9)

2 lo g_{10} (3) (n - 5) (n - 9) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

n - 5 = 0 or n - 9 = 0

Solve

n - 5 = 0 : n = 5

Solve

n - 9 = 0 : n = 9

The solutions to the quadratic equation are:

n = 5, n = 9

6 x^{2} + 6 x - 7 = 0

2 x^{2} - 16 x = - 32

3 - y^{2} = y^{2} + 1

x^{2} + 0 x - 9 = 0

p^{2} + 3 p = 2

What are the solutions to the equation log_{10}(9)(2n^2-14n)=log_{10}(9)(-45+n^2) ?
The solutions to the equation log_{10}(9)(2n^2-14n)=log_{10}(9)(-45+n^2) are n=5,n=9
Find the zeros of log_{10}(9)(2n^2-14n)=log_{10}(9)(-45+n^2)
The zeros of log_{10}(9)(2n^2-14n)=log_{10}(9)(-45+n^2) are n=5,n=9