Final answer:
To solve the logarithmic equation log7(9x) - 2log7(6) = 1, we apply logarithmic properties and ultimately find the exact value of x to be 28/9.
Step-by-step explanation:
The question involves solving an equation with logarithms. The equation given is log7(9x) - 2log7(6) = 1. To solve for x, first apply the logarithm property that states the logarithm of a number raised to an exponent is equal to the exponent times the logarithm of the number:
log7(9x) - log7(62) = 1
Next, rewrite the equation using the property that the logarithm of the division of two numbers is the difference between the logarithms of these numbers:
log7(9x/36) = 1
Raise 7 to the power of both sides of the equation to eliminate the logarithm, finding the exact value of x:
9x/36 = 7
Multiply both sides by 36 and divide by 9 to solve for x:
x = 28/9