What is the answer to log_{7}(x+6)-1=-log_{7}(x) ?

The answer to log_{7}(x+6)-1=-log_{7}(x) is x=1

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log_{7}(x+6)-1=-log_{7}(x)

lo g_{7} (x + 6) - 1 = - lo g_{7} (x)

x = 1

Solution steps

lo g_{7} (x + 6) - 1 = - lo g_{7} (x)

Add

lo g_{7} (x)

to both sides

lo g_{7} (x + 6) - 1 + lo g_{7} (x) = - lo g_{7} (x) + lo g_{7} (x)

Simplify

lo g_{7} (x + 6) - 1 + lo g_{7} (x) = 0

Apply log rules

(x + 6) x = 7

Solve

(x + 6) x = 7 : x = 1, x = - 7

x = 1, x = - 7

Verify Solutions:

x = 1

True

, x = - 7

False

The solution is

x = 1

lo g_{64} (x) = \frac{1}{3}

lo g_{4} (x) = - 1

ln (x - 2) + ln (2 x - 3) = 2 ln (x)

0.912 = ln (x^{3})

ln (x + 2) = 3

What is the answer to log_{7}(x+6)-1=-log_{7}(x) ?
The answer to log_{7}(x+6)-1=-log_{7}(x) is x=1
Solve for x: log_{7}(x+6)-1=-log_{7}(x)
The solution is x=1