solve using a graphing calculator log(base 4)(x+2)-log(base 5)(x-1)=1 e^2x=x+2
Solve `log_4(x+2)-log_5(x-1)=1` :
We can rewrite using the change of base formula: `log_ba=(ln(a))/(ln(b))`
Now we can graph and look for the intersection:
Using the intersect feature we find the solution to be x=2.
This is easily verifiable: `(ln(4))/(ln(4))-(ln(1))/(ln(5))=1-0=1` as required.
(2) Solve `e^(2x)=x+2`
Again we can graph both functions and find the intersection:
The intersect feature gives `x~~.44754216,y~~2.4475422` and `x~~-1.980974,y~~.01902602`