dare to solve this logarithmic problem

let the infinite term be y.then

log7log7y

taking log on an indefinite i.e.,∞ no. gives infinite no. so,

log7log7y = y

nihal what are the given options????

just solve ur self ...the equation is :

y = log₇log₇(Z)

z = \sqrt{z+7}

z^{2} = z + 7

z^{2}-z-7=0

z = \frac{1 +- \sqrt{1^{2} -(4*7*1)}}{2}

z = \frac{1 +-\sqrt{29}}{2}

z = 1 - √292 is discarded as it is less than 1

so z = 1 + √292

wat i mean is , u cant apply analogy anywhere randomly, i hope u get wat i m trying to say

btw if u assumed something , then check whether the ans is within your assumption. i.e , u assumed y to be infintely large, but it actually came out to be 1-3log2 , so the final ans is contradictory to the assumption , so the assumption shud be wrng

i have used here the concept we apply in infinite serirs of resistors or capacitors...u remember.....

taking logarithm on an indefinite number will also be indefinite like 2+∞=∞ and much more....

@ Nihal

Let z = \sqrt{7+\sqrt{7+\sqrt{7+......infinity}}}

Now cover the first square root to get

\sqrt{7+\sqrt{7+......infinity}} which is also equal to z

(i.e.) \sqrt{7+\sqrt{7+......infinity}} = z

Therefore z =\sqrt{7+z}

Square both sides 2 get a quadratic in z

@ nihal , why do u think that y is an infinite number ?

and also , if u assumed it to be an infinite number , did it turn out to be infinite ?

u said log₇log₇y= y

is ur answer y = 1-3log2 satisfying it ?

@ pritishmast i think wat u have done is correct if calc are correct

according to given solution ans will be same for every question like that
i.e. log₇log₇y=y
for any value of y which is an ∞ series
Ex.
y=">

can any one solve this????

how can you take log₇log₇√7+√7+√7....∞ =y
and also √7+√7+√7....∞ =y

solution....

let the infinite term be y.then

log₇log₇y

taking log on an indefinite i.e.,∞ no. gives infinite no. so,

log₇log₇y = y

differentiating both sides w.r.t. y gives

1log₇y X log₇e X 1y X log₇e=1

log7logy X logelog7 X 1y X logelog7=1

1logy.log7.y=1

y.logy=1log7

again differentiating w.r.t. y

1 + logy =0

logy=-1

y=110

y=.1

or y=1-3log2

that is the answer.....

ur steps r right but method seems to be wrong............

answer is not -0.265

hey, (7+......∞)≠(7+8+9+....∞)

dots signify that the series continues....

7+....∞={7+[7+(7+....∞)^1/2]^1/2}^1/2

now solve it..........

hey akhilkona , bad luck....the answer is not 1....

is that 7+.....∞ =7 + 8 + 9 + 10........+ ∞ ???

donno why im getting answer ∞