What is the approximate value of x in the equation below log34 25 3x 1?

To solve for the approximate value of x in the equation log34(25) + 3x = 1, we start by isolating the term with x.

First, we can rewrite the equation to group x:

3x = 1 - log34(25)

Next, we need to evaluate the logarithmic part, log34(25). This logarithm can be calculated using the change of base formula:

log34(25) = log(25) / log(34)

Using a calculator, we find:

• log(25) ≈ 1.39794
• log(34) ≈ 1.53148

Now we can compute:

log34(25) ≈ 1.39794 / 1.53148 ≈ 0.912

Next, substitute this value back into the equation:

3x = 1 - 0.912

This simplifies to:

3x ≈ 0.088

Finally, divide both sides by 3 to solve for x:

x ≈ 0.088 / 3 ≈ 0.02933

So, the approximate value of x is 0.02933.