1.Write the following equation without logs
log y = mx+ c
This would be y = 10^(mx+c) right?
2. Explain why this fits the exponential model (in other words, it can be written in the form y = a x b^x where a and b are real numbers).
1. right
2 compare y = 10^(mx+c) right with y = a(b)^x
a=1, b=10 and x= mx+c
so it fits the model.
To write the equation log y = mx + c without logarithms, you need to rewrite it in exponential form. In exponential form, an equation of the form y = a * b^x represents the exponential model, where a and b are real numbers.
Here's how you can rewrite the equation:
1. Start with the equation log y = mx + c.
2. Use the definition of a logarithm to rewrite it as y = 10^(mx + c). The base 10 is used here because we commonly work with base-10 logarithms (logarithms with base 10 are also known as common logarithms).
3. Apply the exponent laws by using the property 10^(mx + c) = 10^mx * 10^c.
4. Rewrite the equation as y = (10^m)^x * 10^c, which can be further simplified as y = (10^m) * 10^c.
5. Since a real number raised to the power of m is still a real number, let a = 10^m. Therefore, the equation becomes y = a * 10^c, which is in the form of y = a * b^x where b = 10 and a = 10^c.
To summarize, the equation log y = mx + c can be written in the form y = a * b^x where a = 10^c and b = 10. This demonstrates that the equation fits the exponential model.