Solving the Equation: 36 la puterea x = 0.1(6)
In this article, we will solve the equation 36 la puterea x = 0.1(6) and provide a step-by-step guide on how to arrive at the solution.
Understanding the Equation
The given equation is 36 la puterea x = 0.1(6), where "la puterea" is Romanian for "to the power of". Therefore, the equation can be rewritten as:
36^x = 0.1(6)
Simplifying the Equation
First, let's simplify the right-hand side of the equation:
0.1(6) = 0.16
So, the equation becomes:
36^x = 0.16
Taking the Logarithm
To solve for x, we can take the logarithm of both sides of the equation:
log(36^x) = log(0.16)
Using the property of logarithms, we can rewrite the left-hand side as:
x * log(36) = log(0.16)
Solving for x
Now, we can solve for x by dividing both sides by log(36):
x = log(0.16) / log(36)
Calculating the Value of x
Using a calculator, we can find the values of log(0.16) and log(36):
log(0.16) ≈ -0.796 log(36) ≈ 1.556
Substituting these values into the equation, we get:
x ≈ -0.796 / 1.556 x ≈ -0.512
Conclusion
Therefore, the solution to the equation 36 la puterea x = 0.1(6) is x ≈ -0.512.
