Answer:
14 x=3
16 x=3
Step-by-step explanation:
14. 8 * (2/3)^x = 4 (16/27)
Divide by 8 on each side
8/8 * (2/3)^x = 4/8 (16/27)
(2/3)^x = 1/2 * 16/27
(2/3)^x = 8/27
Rewrite 8/27 as 2^3 / 3^3
(2/3)^x = (2/3)^3
If the bases are the same, the exponents have to be the same
x=3
16. (2/5) ^x * (2/5) ^x = 8/125 * 8/125
Take the square root of each side
sqrt[ (2/5) ^x * (2/5) ^x ]= sqrt[8/125 * 8/125]
(2/5)^x = (8/125)
rewrite 8/125 as 2^3/5^3
(2/5)^x = (2/3)^3
If the bases are the same, the exponents have to be the same
x=3
