Question

Which of the following is equivalent to log4^32?

0.4
2.5
1.726
8

Answer 1

The answer will be B. 2.5

Answer 2

Answer. Second option: 2.5

Solution:

log4 32 = x=?

Applying properties of logarithm:

loga b = c → a^c=b

Base of the logaritm: a=4

Exponent: c=x

Power: b=32

log4 32=x→4^x=32

4=2*2→4=2^2

32=2*2*2*2*2→32=2^5

Replacing 4=2^2 and 32=2^5 in the equation above:

4^x=32→(2^2)^x=2^5

Using (a^b)^c=a^(b*c):

(2^2)^x=2^5→2^(2*x)=2^5→2^(2x)=2^5

If the bases are equal in the equation above, the exponents must be equal too:

2x=5

Solving for x. Dividing both sides of the equation by 2:

2x/2=5/2

x=2.5

4^