Make r the subject of the formular: S = ((a(r^n − 1))/(r − 1))


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Question Number 62942 by Tawa1 last updated on 27/Jun/19

$Make r the subject of the formular :$ $S = \frac{a (r^{n} - 1)}{r - 1}$
Commented by Tawa1 last updated on 27/Jun/19

$Sir, help me solve this$ $Find the value of x : 5^{x} + 6 x = 7$
Commented by Tawa1 last updated on 27/Jun/19

$Sir mrW can we use Lanbert function ?$ $Or anybody help .$
Commented by mr W last updated on 27/Jun/19

$n o$
Commented by Tawa1 last updated on 27/Jun/19

$Thank you sir . God bless you$
Commented by mr W last updated on 27/Jun/19

$5^{x} + 6 x = 7$ $5^{x} = 6 (\frac{7}{6} - x)$ $(\frac{7}{6} - x) 5^{- x} = \frac{1}{6}$ $(\frac{7}{6} - x) 5^{\frac{7}{6} - x} = \frac{1}{6} \times 5^{\frac{7}{6}}$ $(\frac{7}{6} - x) e^{(\frac{7}{6} - x) \ln 5} = \frac{1}{6} \times 5^{\frac{7}{6}}$ $[(\frac{7}{6} - x) \ln 5] e^{(\frac{7}{6} - x) \ln 5} = \frac{1}{6} \times 5^{\frac{7}{6}} \times \ln 5$ $\Rightarrow (\frac{7}{6} - x) \ln 5 = W (\frac{1}{6} \times 5^{\frac{7}{6}} \times \ln 5)$ $\Rightarrow x = \frac{7}{6} - \frac{1}{\ln 5} W (\frac{1}{6} \times 5^{\frac{7}{6}} \times \ln 5)$ $\Rightarrow\approx \frac{7}{6} - \frac{0.7933}{\ln 5} = 0.6737$
Commented by kaivan.ahmadi last updated on 27/Jun/19
$5^x =7−6x if we plote y_1 =5^x and y_2 =7−6x then we see that they cut off each othere at one point,this means that this equation has one root. now if f(x)=5^x +6x−7=0 {: ((f(0)<0)),((f(1)>0)) }⇒f(0)f(1)<0 f((1/2))<0 so the root is between ((1/2),1) f((3/4))>0 so the root is between ((1/2),(3/4))$
$5^{x} = 7 - 6 x$ $i f w e p l o t e y_{1} = 5^{x} a n d y_{2} = 7 - 6 x t h e n w e s e e t h a t$ $t h e y c u t o f f e a c h o t h e r e a t o n e p o i n t, t h i s$ $m e a n s t h a t t h i s e q u a t i o n h a s o n e r o o t .$ $n o w i f$ $f (x) = 5^{x} + 6 x - 7 = 0$ $\begin{matrix} f (0) < 0 \\ f (1) > 0 \end{matrix}} \Rightarrow f (0) f (1) < 0$ $f (\frac{1}{2}) < 0$ $s o t h e r o o t i s b e t w e e n (\frac{1}{2}, 1)$ $f (\frac{3}{4}) > 0$ $s o t h e r o o t i s b e t w e e n (\frac{1}{2}, \frac{3}{4})$
Commented by Hope last updated on 27/Jun/19

$f (x) = 5^{x} + 6 x - 7$ $f (0) < 0$ $f (1) = 5^{1} + 6 - 7 > 0$ $f (0.5) = 5^{0.5} + 6 \times 0.5 - 7$ $= 2.23 + 3 - 7 < 0$ $f (0.6) = 5^{0.6} + 6 \times 0.6 - 7$ $= 2.63 + 3.6 - 7 < 0$ $f (0.7) = 5^{0.7} + 6 \times 0.7 - 7$ $= 3.09 + 4.2 - 7 > 0$ $s o v a l u e o f x 0.7 > x > 0.6$
Commented by Tawa1 last updated on 27/Jun/19

$Wow, God bless you sir$
Commented by Tawa1 last updated on 27/Jun/19

$God bless you sir$
Commented by Tawa1 last updated on 27/Jun/19

$God bless you sir$
	Answered by peter frank last updated on 27/Jun/19

	$S r - S = {a r}^{n} - a$ $S r - {a r}^{n} = S - a$ $. . . . . . . . . .$
	Commented by Tawa1 last updated on 27/Jun/19

	$How to find r sir$
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