To approximate the value of y in the equation 10y = 6 using the graph of fx = log10(x), we first need to isolate y in the equation.
1. **Rearranging the Equation:**
We start by dividing both sides by 10. This gives us:
y = 6 / 10
which simplifies to
y = 0.6.
2. **Interpreting the Graph of log10(x):**
The graph of fx = log10(x) helps us to understand how the logarithm function behaves. The output of this function gives us the power to which 10 must be raised to obtain the input value x. For example, if x is 10, then fx = 1, because 101 = 10.
3. **Finding Corresponding Points:**
Now, since we want to find points that relate to y = 0.6, we can substitute this back into the equation in terms of logarithms:
10y = 100.6.
Evaluating 100.6, we can find its approximate value. This essentially translates to finding x where the logarithm equals 0.6.
Graphically, this corresponds to locating y = 0.6 on the vertical axis of the log10(x) graph.
4. **Using the Graph:**
On the graph of fx = log10(x), you can draw a horizontal line at y = 0.6 and see where it intersects the curve of fx. This point of intersection will help us estimate the corresponding value of x.
Observing the graph, if you find that the intersection occurs at approximately x = 4, you can conclude that for y = 0.6 based on our logarithmic equation, the approximation sits nicely around this value.
In conclusion, by rearranging the equation and utilizing the graph of log10(x), we have not only arrived at the value of y = 0.6, but we also engaged with visual data representation to further comprehend its implications!