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:

$y=2^{x+7}$