What is the answer to log_{10}(x+90)=3-log_{10}(x) ?

The answer to log_{10}(x+90)=3-log_{10}(x) is x=10

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log_{10}(x+90)=3-log_{10}(x)

lo g_{10} (x + 90) = 3 - lo g_{10} (x)

x = 10

Solution steps

lo g_{10} (x + 90) = 3 - lo g_{10} (x)

Add

lo g_{10} (x)

to both sides

lo g_{10} (x + 90) + lo g_{10} (x) = 3 - lo g_{10} (x) + lo g_{10} (x)

Simplify

lo g_{10} (x + 90) + lo g_{10} (x) = 3

Apply log rules

(x + 90) x = 1000

Solve

(x + 90) x = 1000 : x = 10, x = - 100

x = 10, x = - 100

Verify Solutions:

x = 10

True

, x = - 100

False

The solution is

x = 10

8 ln (9) = ln (a) + (13 - 1) ln (3)

1 = lo g_{\frac{1}{2}} (x)

lo g_{64} (x) = \frac{4}{3}

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

ln (c x^{6}) = 6 ln (c) + 6 ln (x)

What is the answer to log_{10}(x+90)=3-log_{10}(x) ?
The answer to log_{10}(x+90)=3-log_{10}(x) is x=10
Solve for x: log_{10}(x+90)=3-log_{10}(x)
The solution is x=10