Solve121^5^x-11^1^2^x^+^2 for x x=-2 x=-1 x=2 x=1

Question

Solve
`121^5^x-11^1^2^x^+^2` for x

x=-2
x=-1
x=2
x=1

Answer 1

The solution to the equation
`121^(5x)=11^(12x+2)`, is x=-1, found by expressing 121 as a power of 11, equating the exponents, and solving the resulting linear equation.

To solve the equation
`121^(5x)=11^(12x+2)`, we can use the property of exponents which says that if
`a^(n)=a^(m)`, then n=m, given that a is greater than 0 and not equal to 1.

First, we express 121 as a power of 11, since 121 is the same as
`11^2.`

Our equation thus becomes
`(11^2)^(5x)=11^(12x+2)`.

Applying the rule of exponents that
`(a^m)^n = a^(mn)`, we get
`11^(10x)=11^(12x+2).`

Now we can equate the exponents, which gives us 10x=12x+2.

Solving for x, we subtract 12x from both sides and get -2x=2.

Dividing both sides by -2, we find that x=-1.