Answer to Question #259693 in Algebra for Shy shy

Question

1.8²-×=2

2. (1/2)×←1/8

3. 5×=25×-²

4. 3×+²→8×-¹

5. 4³×=8×-¹

Answer 1

1.

$$8^{2-x}=2$$

$$2^{3(2-x)}=2^1$$

$$6-3x=1$$

$$x=\dfrac{5}{3}$$

2.

$$(\dfrac{1}{2})^{x}=\dfrac{1}{8}$$

$$(\dfrac{1}{2})^{x}=(\dfrac{1}{2})^3$$

$$x=3$$

3.

$$5^{x}=25^{x-2}$$

$$5^x=5^{2(x-2)}$$

$$x=2x-4$$

$$x=4$$

4.

$$3^{x+2}=8^{x-1}$$

$$\ln3^{x+2}=\ln8^{x-1}$$

$$(x+2)\ln3=(x-1)\ln8$$

$$x(\ln8-\ln3)=2\ln3+\ln8$$

$$x=\dfrac{2\ln3+\ln8}{\ln8-\ln3}$$

5.

$$4^{3x}=8^{x-1}$$

$$2^{2(3x)}=2^{3(x-1)}$$

$$6x=3x-3$$

$$x=-1$$