To solve the given equation, we first need to expand the squares in the logarithms.
Using the property that log(a^b) = b*log(a), we get:
2log((7x-9) (7x-9)) + 2log((3x-4) (3x-4)) = 2
Further simplifying, we get:
2log((7x-9)^2) + 2log((3x-4)^2) = 2
Now, we can use the property that log(a) + log(b) = log(ab) to combine the logarithms:
log((7x-9)^2 * (3x-4)^2) = 2
Taking 10 to the power of both sides, we get:
(7x-9)^2 * (3x-4)^2 = 10^2
Expanding both sides, we get:
(49x^2 - 126x + 81) * (9x^2 - 24x + 16) = 100
Expanding further, we get:
441x^4 - 1323x^3 + 1069x^2 - 2016x + 1296 = 100
Rearranging terms and simplifying, we get:
441x^4 - 1323x^3 + 1069x^2 - 2016x + 1196 = 0
Unfortunately, this is a quartic equation and cannot be solved easily by hand. You may need to use numerical methods or a graphing calculator to find the solutions for x.
To solve the given equation, we first need to expand the squares in the logarithms.
Using the property that log(a^b) = b*log(a), we get:
2log((7x-9) (7x-9)) + 2log((3x-4) (3x-4)) = 2
Further simplifying, we get:
2log((7x-9)^2) + 2log((3x-4)^2) = 2
Now, we can use the property that log(a) + log(b) = log(ab) to combine the logarithms:
log((7x-9)^2 * (3x-4)^2) = 2
Taking 10 to the power of both sides, we get:
(7x-9)^2 * (3x-4)^2 = 10^2
Expanding both sides, we get:
(49x^2 - 126x + 81) * (9x^2 - 24x + 16) = 100
Expanding further, we get:
441x^4 - 1323x^3 + 1069x^2 - 2016x + 1296 = 100
Rearranging terms and simplifying, we get:
441x^4 - 1323x^3 + 1069x^2 - 2016x + 1196 = 0
Unfortunately, this is a quartic equation and cannot be solved easily by hand. You may need to use numerical methods or a graphing calculator to find the solutions for x.