Which of the following is equivalent to log4^32? 0.4 2.5 1.726 8

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^

The answer will be B. 2.5

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)

answer: 0.1,0.85

step-by-step explanation: