Question

Which of the following equations would appear as a straight line on a semilog plot? y = 5 exp(2.3x), y = 5 exp(1.1x) + 400, y = (2)^4x, y = 3x^5

Answer 1

`y = 5\cdot e^(2.3\cdot x)`

Explanation:

A semilog plot consist in a logarithmic axis and a linear axis. In this case, the only equation that fulfill the statement conditions of a semilog plot is
`y = 5\cdot e^(2.3\cdot x)`, as it is proved below:

1)
`y = 5\cdot e^(2.3\cdot x)` Given

2)
`y = \ln (5\cdot e^(2.3\cdot x))` Semilog plot

3)
`y = \ln 5 + \ln e^(2.3\cdot x)`
`\ln (a\cdot b) = \ln a + \ln b`

4)
`y = \ln 5 + 2.3\cdot x \cdot \ln e`
`\ln a^(b) = b\cdot \ln a`

5)
`y = \ln 5 + 2.3\cdot x`
`\ln e = 1`/Modulative property/Result