Question

121^x-2*11^x+1=0 решите показательное уравнение

Answer 1

$121^x-2*11^x+1=0 \\ (11^x-1)^2=0 \\ 11^x-1=0 \\ 11^x=1 \\ 11^x=11^0 \\ x=0$

Answer 2

I can help you solve the exponential equation 121^x-2*11^x+1=0. Here are the steps:

- First, we need to rewrite the equation in the form of a^x=b, where a and b are constants. To do this, we can divide both sides by 121^x and use the property that (a/b)^x=a^x/b^x. We get:

(121^x-2*11^x+1)/121^x=0

(1-2*(11/121)^x+(1/121)^x)=0

- Next, we can make a substitution: let y=(11/121)^x. Then the equation becomes:

1-2*y+y^2=0

- This is a quadratic equation, which we can solve by using the quadratic formula:

y=(-b±√(b^2-4ac))/(2a)

y=(-(-2)±√((-2)^2-4*1*1))/(2*1)

y=(2±√(4-4))/2

y=(2±0)/2

y=1

- Now we need to find the value of x that satisfies y=(11/121)^x. To do this, we can take the logarithm of both sides and use the property that log_a(b)=x if and only if a^x=b. We get:

log_(11/121)(y)=x

log_(11/121)(1)=x

0=x

- Therefore, the solution of the exponential equation is x=0. You can check this by plugging it back into the original equation and see that it is true.

I hope this helps you understand how to solve exponential equations. If you need more help, you can use some online calculators that can solve equations for you, such as [Symbolab](https://ru.symbolab.com/solver/equation-calculator), [Mathway](https://www.mathway.com/algebra) or [Mathway in Russian](https://www.mathway.com/ru/Algebra). You can also find more examples and explanations on how to solve exponential equations on [this website](https://www.kontrolnaya-rabota.ru/s/equal-one/any-uravnenie/e/x_v_stepeni_dva_minus_sto_dvadczat_odin_ravno_nol/).