What is the answer to 7^{xlog_{7}(x-2)}=x-2 ?

The answer to 7^{xlog_{7}(x-2)}=x-2 is x=3

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7^{xlog_{7}(x-2)}=x-2

7^{x l o g_{7} (x - 2)} = x - 2

x = 3

Solution steps

7^{x l o g_{7} (x - 2)} = x - 2

Apply log rules

lo g_{7} (x - 2) (x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

lo g_{7} (x - 2) = 0 or x - 1 = 0

Solve

lo g_{7} (x - 2) = 0 : x = 3

Solve

x - 1 = 0 : x = 1

Verify Solutions:

x = 3

True

, x = 1

False

The solution is

x = 3

lo g_{x} (1296) = 4

- 2 ln (x) + 1 = 0

lo g_{5 x} (x + 1) = \frac{8}{3}

lo g_{3} ((x - 2)^{2}) = 14

lo g_{10} (3 z) = 2

What is the answer to 7^{xlog_{7}(x-2)}=x-2 ?
The answer to 7^{xlog_{7}(x-2)}=x-2 is x=3
Solve for x: 7^{xlog_{7}(x-2)}=x-2
The solution is x=3