Determine m: 4^(4m) = 4^8+4^8+4^8+4^8
4^(4m) = 4^8+4^8+4^8+4^8
4^(4m)=4^8(1+1+1+1)
4^(4m)=4^8.4^1
4^(4m)=4^9
4m=9
M=9/4
4^(4m) = 262,144
4m*Log4 = Log262144
Divide both sides by Log 4:
4m = 9
m = 9/4.
To solve this equation, we need to apply the property of exponents which states that when you have the same base raised to different powers and they are multiplied, you can add the exponents. In this case, we have 4^8 being added four times, which can be written as:
4^(4m) = 4^8 + 4^8 + 4^8 + 4^8
To simplify this equation, we start by combining the exponents on the right side of the equation:
4^(4m) = 4^(8 + 8 + 8 + 8)
Next, we use the property of exponents to add the exponents on the right side:
4^(4m) = 4^(32)
Since the bases are the same on both sides of the equation, we can equate the exponents:
4m = 32
To solve for m, we divide both sides of the equation by 4:
m = 32 / 4
m = 8
Therefore, m is equal to 8.