Question

A^(5-x)(3x-1)=1a в степени (5-x)(3x-1)= 1

Answer 1

A^(5-x)(3x-1)=1
a^(5-x)(3x-1) = a^0
(5-x)(3x-1)=0
5-x=0
x1=5
3x-1=0
3x=1
x2=1/3

Answer 2

To solve for x in the equation:

A^(5-x)(3x-1) = 1

We can start by noticing that any non-zero number raised to the power of zero is equal to one. Therefore, if A is not equal to one, we can rewrite the equation as:

A^(5-x) = 1 / (3x - 1)

Now, we can use the fact that the logarithm of a number raised to a power is equal to the product of the power and the logarithm of the number. So, taking the logarithm of both sides of the equation with base A, we get:

(5 - x) log(A) = log[1 / (3x - 1)]

Using the fact that log(1/a) = -log(a), we can simplify the right-hand side:

(5 - x) log(A) = -log(3x - 1)

Dividing both sides by log(A) and multiplying by -1, we get:

x = (log(3x - 1)) / log(A) - 5

Note that this solution is valid only if A is not equal to one, because in that case we would have:

A^(5-x)(3x-1) = 1^(5-x)(3x-1) = 1*(3x-1) = 3x-1

And we would obtain a linear equation, which is easy to solve:

3x - 1 = 1

3x = 2

x = 2/3

So the solution to the equation depends on whether A is equal to one or not.