Question

Find the approximate irrational solution to 3^x = 6

Answer 1

To find the approximate irrational solution to 3^x = 6, we can use logarithms. Taking the logarithm base 3 of both sides of the equation, we get x log 3 = log 6. Dividing both sides by log 3, we find x = log 6 / log 3.

Step-by-step explanation:

To find the approximate irrational solution to 3^x = 6, we can use logarithms. Taking the logarithm base 3 of both sides of the equation, we get x log 3 = log 6. Dividing both sides by log 3, we find x = log 6 / log 3. Using a calculator to evaluate this, we find that x is approximately 1.6309.

Answer 2

Step-by-step explanation:

We can use logarithms to solve for x. Taking the logarithm of both sides of the equation 3^x = 6 gives:

log(3^x) = log(6)

Using the property of logarithms that states log(a^b) = b*log(a), we can simplify the left side of the equation:

x*log(3) = log(6)

Then, we can isolate x by dividing both sides by log(3):

x = log(6) / log(3)

Using a calculator to approximate the values of the logarithms, we get:

x ≈ 1.6309

Therefore, the approximate irrational solution to 3^x = 6 is x ≈ 1.6309.