Question

determine the value of y for each of the following.
a) \\(\log_y 49 = 2\\)
value

b) \\(\log_{25} y = \frac{1}{2}\\)
value

c) \\(\log_6 216 = y\\)
value

Explanation:

Part (a)

Step1: Recall log definition

If $\log_{y}49 = 2$, by definition of logarithm, $y^{2}=49$.

Step2: Solve for y

Take square root: $y=\sqrt{49}=7$ (since base $y>0,y
eq1$).

Step1: Recall log definition

If $\log_{25}y=\frac{1}{2}$, then $25^{\frac{1}{2}}=y$.

Step2: Simplify exponent

$25^{\frac{1}{2}}=\sqrt{25}=5$, so $y = 5$.

Step1: Recall log definition

If $\log_{6}216=y$, then $6^{y}=216$.

Step2: Express 216 as power of 6

$6^{3}=216$, so $y = 3$.

Answer:

7

Part (b)