Make-r-the-subject-of-the-formular-S-a-r-n-1-r-1-

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 - 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

\dots \dots \dots .

Commented by Tawa1 last updated on 27/Jun/19

How to find r sir

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