Question

0.1*log^4(10,x)-log^2(10,x)+0.9=0

Answer 1

Ответ:

Объяснение:

log^4(10,x) = t

0.1t^2 - t +0.9 = 0

D = 4*0.1*0.9 = 0.64

t1 = 1+0.8 / 0.2 = 9

t2 = 1

log^2(10, x) = 9 => lgx = 9

log^2(10, x) = 1 => lgx =1

x1 = 10^9

x2 = 10

Answer 2

We can simplify the equation using the following substitution: let y = log(10,x). Then the equation becomes:

0.1*y^4 - y^2 + 0.9 = 0

This is a quadratic equation in y^2. We can solve for y^2 using the quadratic formula:

y^2 = [ -(-1) ± sqrt((-1)^2 - 4(0.1)(0.9)) ] / (2*0.1)

y^2 = [ 1 ± sqrt(1 - 0.36) ] / 0.2

y^2 = [ 1 ± sqrt(0.64) ] / 0.2

y^2 = [ 1 ± 0.8 ] / 0.2

y^2 = 5 or y^2 = 0.2

Since y = log(10,x), we have:

log(10,x) = sqrt(5) or log(10,x) = sqrt(0.2)

We can solve for x by taking the inverse logarithm of both sides:

x = 10^(sqrt(5)) or x = 10^(sqrt(0.2))

These are the exact solutions to the equation. However, if you need numerical approximations, you can use a calculator to find:

x ≈ 316.228 or x ≈ 1.58489