What is the answer to log_{5x}(x+1)= 8/3 ?

The answer to log_{5x}(x+1)= 8/3 is x\approx 0.21516…

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log_{5x}(x+1)= 8/3

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

x \approx 0.21516 \dots

Solution steps

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

Apply log rules

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

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

ln (x + 1) \cdot 3 = ln (5 x) \cdot 8

Apply log rules

(x + 1)^{3} = 390625 x^{8}

Solve

(x + 1)^{3} = 390625 x^{8} : x \approx - 0.18521 \dots, x \approx 0.21516 \dots

x \approx - 0.18521 \dots, x \approx 0.21516 \dots

Verify Solutions:

x \approx - 0.18521 \dots

False

, x \approx 0.21516 \dots

True

The solution is

x \approx 0.21516 \dots

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

lo g_{10} (3 z) = 2

lo g_{a} (\frac{1}{16}) = 2

lo g_{3} (x^{2}) = 1

ln (\frac{760}{x}) = 0.002192398

What is the answer to log_{5x}(x+1)= 8/3 ?
The answer to log_{5x}(x+1)= 8/3 is x\approx 0.21516…
Solve for x: log_{5x}(x+1)= 8/3
The solution is x\approx 0.21516…