What is |log_{1/5}(x+1)|+log_{5}(x+2)<1 ?

The solution to |log_{1/5}(x+1)|+log_{5}(x+2)<1 is -3/4 <x<(sqrt(21)-3)/2

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|log_{1/5}(x+1)|+log_{5}(x+2)<1

lo g_{\frac{1}{5}} (x + 1) + lo g_{5} (x + 2) < 1

- \frac{3}{4} < x < \frac{21 - 3}{2}

Interval Notation

(- \frac{3}{4}, \frac{21 - 3}{2})

Decimal Notation

- 0.75 < x < 0.79128 \dots

Solution steps

lo g_{\frac{1}{5}} (x + 1) + lo g_{5} (x + 2) < 1

Find positive and negative intervals

x < - 1, - 1 \leq x \leq 0, x > 0

Solve the inequality for each interval

- \frac{3}{4} < x \leq 0 or 0 < x < \frac{21 - 3}{2}

Merge Overlapping Intervals

- \frac{3}{4} < x < \frac{21 - 3}{2}

- 18 x^{2} + 34 x - 23 \leq 0

- 6 (1 - 5 v) = 54

3 x^{2} + 2 x - 5 = 0

\frac{1}{6} + 1

(- \frac{3}{4})^{2}

What is |log_{1/5}(x+1)|+log_{5}(x+2)<1 ?
The solution to |log_{1/5}(x+1)|+log_{5}(x+2)<1 is -3/4 <x<(sqrt(21)-3)/2