Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Exponential Equation

How is this done?

Solve for x.

3^(9x) = 9^(3x)

I am thinking about taking the log on both sides.

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Exponential Equation

Normally I'd say yes  but if you do the x cancel out and you're left with an inconsistency.

Just checking Wolfram Alpha

Back again. As suspected WA gives x=0 as the only real solution.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Exponential Equation

Normally I'd say yes  but if you do the x cancel out and you're left with an inconsistency.

Just checking Wolfram Alpha

Back again. As suspected WA gives x=0 as the only real solution.

Bob

Now that we know that x = 0 is the only real solution, how do we find x?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Exponential Equation

The inconsistency shows I've performed an illegal act so that suggests I cannot cancel as that's really division by zero. That leads to the possibility that x=0. Then check it fits. Anything^0 =1 so LHS = RHS = 0. It works.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Exponential Equation

The inconsistency shows I've performed an illegal act so that suggests I cannot cancel as that's really division by zero. That leads to the possibility that x=0. Then check it fits. Anything^0 =1 so LHS = RHS = 0. It works.

Bob

Copy. Moving on....