To solve this equation, we can use the properties of logarithms.
First, we can combine the logarithms on the left side of the equation using the properties of logarithms: log4(x^2) + logx^6 64 = 2 log4(x^2 * x^6) = 2 log4(x^8) = 2
Next, we can rewrite the equation in exponential form: 4^2 = x^8 16 = x^8
Taking the 8th root of both sides gives us the final solution: x = ±2
Therefore, the solution to the equation log4(x^2) + logx^6 64 = 2 is x = ±2.
To solve this equation, we can use the properties of logarithms.
First, we can combine the logarithms on the left side of the equation using the properties of logarithms:
log4(x^2) + logx^6 64 = 2
log4(x^2 * x^6) = 2
log4(x^8) = 2
Next, we can rewrite the equation in exponential form:
4^2 = x^8
16 = x^8
Taking the 8th root of both sides gives us the final solution:
x = ±2
Therefore, the solution to the equation log4(x^2) + logx^6 64 = 2 is x = ±2.