Question

Which equation is equivalent to log(base 2)y = x + 7?y=2^(x + 7)y=2^x +7y=(x + 7)

Answer 1

Given the logarithmic equation

`\log _2y=x+7`

To determine an equivalent equation, we convert the equation from logarithm form to index form using the rule below.

`\begin{gathered} If\; \log _ab=c,\text{ then:} \\ a^c=b \end{gathered}`

Therefore:

`\log _2y=x+7\equiv y=2^(x+7)`

The equivalent form of the given equation is:

`y=2^(x+7)`