To solve the equation, we can use the properties of logarithms to simplify the expression:
log3 X + 2log3 (9X) = 7
Use the power rule of logarithms: log_a (A^n) = n * log_a (A)
log3 X + log3 ((9X)^2) = 7log3 X + log3 (81X^2) = 7
Combine the logarithms using the product rule: log_a (A) + log_a (B) = log_a (A*B)
log3 (X * 81X^2) = 7log3 (81X^3) = 7
Rewrite the equation in exponential form: a^b = c is equivalent to log_a c = b
3^7 = 81X^3
Solve for X:
2187 = 81X^3
Divide both sides by 81:
27 = X^3
Take the cube root of both sides:
X = 3
Therefore, the solution to the equation log3 X + 2log3 (9X) = 7 is X = 3.
To solve the equation, we can use the properties of logarithms to simplify the expression:
log3 X + 2log3 (9X) = 7
Use the power rule of logarithms: log_a (A^n) = n * log_a (A)
log3 X + log3 ((9X)^2) = 7
log3 X + log3 (81X^2) = 7
Combine the logarithms using the product rule: log_a (A) + log_a (B) = log_a (A*B)
log3 (X * 81X^2) = 7
log3 (81X^3) = 7
Rewrite the equation in exponential form: a^b = c is equivalent to log_a c = b
3^7 = 81X^3
Solve for X:
2187 = 81X^3
Divide both sides by 81:
27 = X^3
Take the cube root of both sides:
X = 3
Therefore, the solution to the equation log3 X + 2log3 (9X) = 7 is X = 3.