soccergal12 2 years ago solve the following: 10^(2x-3) = 0.01

1. klimenkov

If $$a^x=b^x$$, then $$a=b$$. And use $$0.01=\frac1 {100}=\frac1{10^2}=10^{-2}$$.

2. klimenkov

Oops. Really you need is that if $$a^x=a^y$$ then $$x=y$$.

3. Calcmathlete

Use what @klimenkov said above. $10^{2x - 3} = 0.01$$10^{2x - 3} = \frac{1}{100}$$10^{2x - 3} = \frac{1}{10^{2}}$$10^{2x - 3} = 10^{-2}$$2x - 3 = -2$Solve for x now.

4. klimenkov

The very first statement is false. Forget it, because if $$2^2=(-2)^2$$, but $$2\ne-2$$.

5. Calcmathlete

What do you mean? I'm not quite following.

6. klimenkov

I said that mine statement was false.

7. Calcmathlete

Oh ok.

8. soccergal12

i'm sorry. which statement was false?

9. soccergal12

would the answer be x = 1/2

10. theyatin

yup

11. soccergal12

Thanks!

12. Calcmathlete

I am so late...but you are correct :)