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.

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

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

$6x=3x-3$

$x=-1$