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^