3 log 6 x +5 log 6 (x-6)?

3log[6](x)+5log[6](x-6)

=log[6](x)^3+log[6](x-6)^5

=log[6](x^3(x-6)^5) answer//

A. Given: log(3x+8) - log(2x-5) = 2 we'd p.c. to remedy for x. via employing some rules of logarithms to the expression on the left-hand part, we acquire log[(3x + 8) / (2x - 5)] = 2. This tells us that, 10^ { log[(3x + 8) / (2x - 5)] } = 10^2, this is (3x + 8) / (2x - 5) = a hundred. Equivalently, 3x + 8 = a hundred (2x - 5). = 200x - 500. So, 3x - 200x = -500 - 8 -197x = -508 x = 508 / 197, that's approximately 2.578. observe that the value of x is a answer of the given equation if and on condition that: log(3x + 8) is a actual selection on each and every occasion 3x + 8 > 0, i.e. x > -8/3 and log(2x - 5) is a actual selection on each and every occasion 2x - 5 > 0, i.e. x > 5/2. considering the two inequalities would desire to be happy, it means that x > 5/2 = 2.5. through fact our x interior the above equation yields 508 / 197 > 2.5, it follows that x is a answer of the given equation. B. Given: log(x-5) + log(x+9) + log(x-6) + log(x-3) If we prepare some rules on logarithms, we can only SIMPLIFY this into an expression with basically one term, this is: log [(x - 5)(x + 9)(x - 6)(x - 3)].

3log_6(x) + 5log_6(x - 6)
= log_6(x^3) + log_6[(x - 6)^5]
= log_6[x^3 * (x - 6)^5]
= log_6[x^3(x - 6)^5]

3log(6x) = log(6x)^3

5log[6(x-6)] = log[6(x-6)] ^5

now put this in the above expression.

log(6x)^3 + log[6(x-6)]^5

now use addition law for log we have reduced it to one term

log{ (6x)^3 * [6(x-6)]^5 }

further simplifying

log{ 6^8*x^3*(x-6)^5 }..............answer

= log 6 x^3 + log 6 (x-6)^5
= log 6 [x^3(x-6)^5]