Solve Log EQ: log3^(2x-9)-2xlog3=-2

[juliany]

Homework Statement

Solve: log3^(2x-9)-2log3^x=-2

Homework Equations

None

The Attempt at a Solution

I am confused with one part of this equation.
With the 2log3^x, can you move the x to the front to make it 2x log3?

 

[dx]

Yes, that's valid.

 

[juliany]

So that would make it 2x-9log3-2xlog3=-2
Therefore: 2x-9-2x=-2?

 

[dx]

where did the log 3 go in your last step?

 

[juliany]

Woops, was thinking the same base rule.

Can you go: log3^(2x-9)-log3^x^2=-2
Therefore: Log3 (2x-9)/x^2=-2?

 

[dx]

$$2 \log 3^{x}$$ is $$\log 3^{2x}$$. Just to make sure, was this the original equation?

$$\log3^{2x-9}-2\log 3^x=-2$$​

Because it cannot be solved for x.

 

[juliany]

Yes it was, how did you figure out that you can't solve for x?

 

[dx]

Using the rule $\log a^{b} = b \log a$, the equation becomes $$(2x - 9 - 2x) \log 3 = - 2$$, and the 2x and -2x cancel out. Then you get the equation $$\log 3 = 2/9$$. This is true for an appropriate base of the logarithm, which you can find using a log table.

 

[juliany]

Ok, thanks a lot.