I really need help with these three questions!!!!!

Question

log3(81) = ?. Just type the number, and nothing else. Hint: Notice that 81 is a power of 3.

 
Since 3^4 = 81, log3(81) = ?. Just type the number, and nothing else.

 
log4(32) = ?. Your answer will be a fraction.  Hint: Notice that both 4 and 32 are powers of 2.

Answer 1

Ask your self this question.  3 raised to what power results in 81?

 

3^x = 81

 

where  x is the power.

 

3⁴ = 81

 

log₃(81) = 4

 

 

log₄(32)

 

4 raised to what power results in 32?

 

4^p = 32

 

Solve for p.  Rewrite this equation using common bases.

 

(2²)^p = 2⁵

 

 

Using the rule of exponents.

 

2^2p = 2⁵

 

 

Equate the exponents.

 

2p = 5

 

 p = 5/2

 

 

log₄(32) = 5/2