How do I solve this: Log3(X-4) = Log9(X+1) ?

[alexMATH]

Log₃(X-4)=Log₉(X+1)

Any help is much appreciated.

 

[mmm4444bot]

Log₃(X-4)=Log₉(X+1)

Logarithms are exponents. Let's pick a symbol to represent the exponent inferred above. I'll use Z.

Z = Log₃(X - 4)

Z = Log₉(X + 1)

This is a system of two equations. Switch them to exponential form.

Then, realizing that 9 can be written as 3^2, see if you can use substitution to form a quadratic equation to solve for X.

If you would like more help, please show us what you've done so far or explain why you're stuck. :cool:

 

[stapel]

How do I solve this?

Log₃(X-4)=Log₉(X+1)

Try using the change-of-base formula (here) on the right-hand side, using the fact that log₃(9) = 2. Then use basic log rules (here) to convert the right-hand side to a log, base three, of a square root. Then you can set the arguments of the two logs equal, and solve the resulting radical equation.