What is the answer to log_{10}(x+2)=2-log_{10}(x) ?

The answer to log_{10}(x+2)=2-log_{10}(x) is x=-1+sqrt(101)

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log_{10}(x+2)=2-log_{10}(x)

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

x = - 1 + 101

Decimal Notation

x = 9.04987 \dots

Solution steps

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

Add

lo g_{10} (x)

to both sides

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

Simplify

lo g_{10} (x + 2) + lo g_{10} (x) = 2

Apply log rules

(x + 2) x = 100

Solve

(x + 2) x = 100 : x = - 1 + 101, x = - 1 - 101

x = - 1 + 101, x = - 1 - 101

Verify Solutions:

x = - 1 + 101

True

, x = - 1 - 101

False

The solution is

x = - 1 + 101

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

- lo g_{10} (x) = 9.44

10 lo g_{10} (x) = 4

10 lo g_{10} (x) = 0

4 - 3 ln (x) = 3

What is the answer to log_{10}(x+2)=2-log_{10}(x) ?
The answer to log_{10}(x+2)=2-log_{10}(x) is x=-1+sqrt(101)
Solve for x: log_{10}(x+2)=2-log_{10}(x)
The solution is x=-1+sqrt(101)