Question

Solve the equation using propertis of logarithms and exponents.

9^6x=3^2x+4

Answer 1

To solve the equation 9^6x = 3^2x+4, rewrite 9 as 3^2, apply exponent rules to get a single power of 3 on each side, set the exponents equal since the bases are the same, and solve for x, resulting in x = 2/5 as the solution.

Step-by-step explanation:

To solve the equation 9^6x = 3^2x+4 using properties of logarithms and exponents, we can follow these steps:

1. Recognize that 9 is a power of 3, specifically, 9 = 3^2. Therefore, we can rewrite the equation as (3^2)^(6x) = 3^(2x+4).
2. Using the property that (a^b)^c = a^(b*c), we rewrite the left side of the equation as 3^(2*6x) or 3^(12x).
3. Now the equation is 3^(12x) = 3^(2x+4). Since the bases are the same, we can set the exponents equal to each other: 12x = 2x + 4.
4. Solving for x, subtract 2x from both sides to get 10x = 4.
5. Finally, divide by 10 to get x = 4/10 or x = 2/5.

Answer 2

9^(6x)=3^(2x+4) I assume this is what you meant...

since 9=3^2

3^2^(6x)=3^(2x+4)

and since (a^b)^c=a^(bc)

3^(12x)=3^(2x+4)

so if a^b=a^c then b=c so

12x=2x+4

10x=4

x=0.4