Solve the equation $2^{3x+4} = 4 \sqrt 2$

Question

Help??????

Before hand I had to write sqrt $2$ as a power of $2$ then express $4$ $\sqrt 2$ as a power of $2$. How to solve the above equation I am not too sure!?

can you state what you already tried? – user93089 Sep 27 '13 at 15:28 — user93089, Sep 27 '13 at 15:28

score 6 · Answer 1 · answered Sep 27 '13 at 15:17

6

I assume that it is supposed to be $$2^{3x+4}=4\sqrt 2.$$ After writing $4=2^2$ and $\sqrt 2=2^\frac12,$ we find that $$4\sqrt 2=2^{2+\frac12}=2^{\frac52},$$ so $$2^{3x+4}=2^{\frac52}.$$ What can we do now?

answered Sep 27 '13 at 15:17

Cameron Buie

102,994

score 4 · Answer 2 · answered Sep 27 '13 at 15:25

4

HINT:

$4\sqrt2$$= 2^{\frac52}=2^{3x+4}$.

Equate the powers and VOILA.

answered Sep 27 '13 at 15:25

Shobhit

6,902

VOILA! nice thing. – Silent Sep 27 '13 at 15:50

score 2 · Answer 3 · answered Sep 27 '13 at 15:25

2

Hint: $2^a=2^b\implies a=b, a\in\mathbb{R},b\in\mathbb{R}.$

answered Sep 27 '13 at 15:25

Sujaan Kunalan

10,944

Solve the equation $2^{3x+4} = 4 \sqrt 2$

3 Answers3