Question

1.
a) $log_{2}128 =$

b) $log_{8}64 = 2$

c) $log_{3}\frac{1}{27} =$

instructions: ev
3.
a) $log_{6}36 = $

b) $log_{2}32 = $

c) $log_{4}64 = $

d) $log_{3}81 = $

instructions
5.
$log_{16}$

Explanation:

Step1: Rewrite 128 as $2^7$

$\log_{2}128 = \log_{2}2^7$

Step2: Apply log power rule $\log_b b^x=x$

$\log_{2}2^7 = 7$

Step3: Rewrite 64 as $8^2$

$\log_{8}64 = \log_{8}8^2$

Step4: Apply log power rule

$\log_{8}8^2 = 2$

Step5: Rewrite $\frac{1}{27}$ as $3^{-3}$

$\log_{3}\frac{1}{27} = \log_{3}3^{-3}$

Step6: Apply log power rule

$\log_{3}3^{-3} = -3$

Step7: Rewrite 36 as $6^2$

$\log_{6}36 = \log_{6}6^2$

Step8: Apply log power rule

$\log_{6}6^2 = 2$

Step9: Rewrite 32 as $2^5$

$\log_{2}32 = \log_{2}2^5$

Step10: Apply log power rule

$\log_{2}2^5 = 5$

Step11: Rewrite 64 as $4^3$

$\log_{4}64 = \log_{4}4^3$

Step12: Apply log power rule

$\log_{4}4^3 = 3$

Step13: Rewrite 81 as $3^4$

$\log_{3}81 = \log_{3}3^4$

Step14: Apply log power rule

$\log_{3}3^4 = 4$

Answer:

1. A) $7$
2. B) $2$
3. C) $-3$
4. A) $2$
5. B) $5$
6. C) $3$
7. D) $4$