Question

What is the exact value of x in equation 5⋅21x⁵ = 16 ?

a) x=5log ₂₁/log ₃.₂
b) x=log ₂₁/5log ₃.₂
c) x=5log ₃.₂/log ₂₁
d) x=log ₃.₂/5log ₂₁

Answer 1

To find the value of x in the equation 5⋅21x⁵ = 16, you can use logarithms. The exact value of x is x = e^((ln(16) - ln(5))/5)/21.

Step-by-step explanation:

To find the value of x in the equation 5⋅21x⁵ = 16, we can use logarithms. Taking the natural logarithm of both sides of the equation, we get:

ln(5⋅21x⁵) = ln(16)

Using the property of logarithms that ln(a⋅b) = ln(a) + ln(b), we can rewrite the equation as:

ln(5) + ln(21x⁵) = ln(16)

Simplifying further, we can rewrite the equation as:

ln(5) + 5ln(21x) = ln(16)

Now we can isolate the term with x:

5ln(21x) = ln(16) - ln(5)

Dividing both sides by 5:

ln(21x) = (ln(16) - ln(5))/5

Now we can apply the inverse natural logarithm function to both sides to solve for x:

21x = e^((ln(16) - ln(5))/5)

Dividing both sides by 21:

x = e^((ln(16) - ln(5))/5)/21

So the exact value of x in the equation 5⋅21x⁵ = 16 is x = e^((ln(16) - ln(5))/5)/21.