Logarithms Logarithms

Question

Find the largest value of x that satisfies: 

log₅(x²)-log₅(x+3)=9

Answer 1

Madina

Well if you simplify the left hand side you will get log ₅ ( x²/ x+3 ) using the rules of logs.

This equals 9.

Raising 5 to both sides of the equation gives, x² / (x+3) = 5⁹ = 1953125

Now x² / x+3 is approximately x²/ x = x. (In fact it will be slightly less).

So the solution for x will be approximately 1953125.

So I suggest you try trial and error - try x = 1953126, 1953127 .... until you find a solution that fits the above equation.

Mike