Solving the Logarithmic equation $\log_x (3-2\sqrt2)=2$

Question

$$\log_x (3-2\sqrt2)=2$$ I can't solve it, I tried everything but I can't find the solution I tried logarithmic properties but nothing works, please help!

TeX: prefix the log with a backslash to make it upright: \log $\log$ vs. log $log$. — CiaPan, Jul 13 '15 at 13:01
How about taking the square root of 3-2(surd2) that is if the equation is transformed from logarithmic to exponential. — Dr. NGILAZI BANDA, Jul 13 '15 at 15:37

score 8 · Answer 1 · answered Jul 13 '15 at 13:01

8

You can simply re-write with logarithm rules: $$x^2=3-2\sqrt2$$ because $$\log_ba=c \Leftrightarrow b^c=a$$

And the answer is as simple as taking the root.

answered Jul 13 '15 at 13:01

Terra Hyde

1,102

score 1 · Accepted Answer · answered Jul 13 '15 at 13:40

1

I may banned after this comment, but technic might be helpful.

If you have had: $$ 3 + 2 \cdot \sqrt{2} $$ You would be see: $$ (\sqrt{2} + 1)^2 $$ And carefully do calculations you may provide that this statements are the same.

answered Jul 13 '15 at 13:40

Dmytro Chasovskyi

373

Solving the Logarithmic equation $\log_x (3-2\sqrt2)=2$

2 Answers2