Question

1)25^x=125 2)4^2x-12=1 3)9^x=1/27 4)4^x+2^x+1=80 Pl

Answer 1

1)5^2x=5³
2x=3
x=1,5
2)2x-12=0
2x=12
x=6
3)3^2x=3^-3
2x=-3
x=-1,5
4)4^x+2*2^x-80=0
2^x=a
a²+2a-80=0
a1+a2=-2 u a1*a2=-80
a1=-10⇒2^x=-10 нет решения
a2=8⇒2^x=8⇒⇒x=3

Answer 2

1. Solving for x in the equation 25^x = 125: Rewrite 125 as 5^3. 25^x = 5^3 Rewrite both sides using the same base, which is 5. (5^2)^x = 5^3 Apply the exponent property: (a^b)^c = a^(b*c). 5^(2x) = 5^3 Equate the exponents: 2x = 3 Solve for x: x = 3/2 or x = 1.5

2. Solving for x in the equation 4^(2x) - 12 = 1: Add 12 to both sides of the equation: 4^(2x) = 13 Rewrite 13 as 4 + 9. 4^(2x) = 4^2 + 3^2 Apply the exponent property: a^(b+c) = a^b * a^c. 4^(2x) = 4^2 * 3^2 Equate the exponents: 2x = 2 * 2 + 2 * 2 Simplify the right side: 2x = 4 + 4 2x = 8 Solve for x: x = 4

3. Solving for x in the equation 9^x = 1/27: Rewrite 1/27 as (1/3)^3. 9^x = (1/3)^3 Rewrite both sides using the same base, which is 3. (3^2)^x = (1/3)^3 Apply the exponent property: (a^b)^c = a^(b*c). 3^(2x) = (1/3)^3 Apply the exponent property: (1/a)^b = a^(-b). 3^(2x) = 3^(-3) Equate the exponents: 2x = -3 Solve for x: x = -3/2 or x = -1.5

4. Solving for x in the equation 4^x + 2^x + 1 = 80: Subtract 1 from both sides of the equation: 4^x + 2^x = 79 Rewrite 79 as 64 + 16 - 1. 4^x + 2^x = 4^3 + 2^4 - 1 Apply the exponent property: a^x + a^y = a^(x+y). 4^x + 2^x = 4^(3+4) - 1 Simplify the exponents on the right side: 4^x + 2^x = 4^7 - 1 Since the bases are the same, equate the exponents: x = 7

Please note that these solutions are approximate values and may be rounded depending on the level of precision required.