To approximate the value of y in the equation 10y = 5 using the graph of f(x) = log₁₀(x), follow these steps:
- Solve for y: First, start by simplifying the equation. We can rewrite it as:
- y = log₁₀(5). This transformation is derived from the property of logarithms that states if a = b, then log₁₀(a) = log₁₀(b).
- Identify the logarithmic value: Now, you want to find log₁₀(5). To do this using the graph of f(x) = log₁₀(x), look for the value of x = 5 on the horizontal axis.
On the graph:
- Locate the point where x = 5. Follow the vertical line up to meet the curve of f(x).
- Read the corresponding y value from the vertical axis. This is your approximation for log₁₀(5).
To provide a numerical value for y, we know through calculators that:
- log₁₀(5) ≈ 0.699.
Therefore, substituting this back gives:
- y ≈ 0.699.
In conclusion, using the graph of f(x) = log₁₀(x), you can approximate y in the equation 10y = 5 as approximately 0.699.