Question

If 512^x = 64^240, then x = __.

Answer 1

Step-by-step explanation:

2^9x = 2^1440

9x = 1440

x= 160

Answer 2

Answer:

160

Step-by-step explanation:

64 = 8 x 8 = 8²

so 64 ²⁴⁰  =  ( 8 x 8 ) ²⁴⁰

= ( 8² )²⁴⁰ = 8⁴⁸⁰     [  because (aᵇ)ⁿ = (a)ᵇⁿ  ]

512 = 8 x 8 x 8 = 8³

so 512ˣ = ( 8 x 8 x 8 )ˣ = (8³)ˣ = 8³ˣ          [  because (aᵇ)ⁿ = (a)ᵇⁿ  ]

512ˣ = 64 ²⁴⁰ ( given )

so 8³ˣ = 8⁴⁸⁰     [ because 512ˣ = 8³ˣ    and   64 ²⁴⁰ = 8⁴⁸⁰ ]

=> 3x = 480      

=> x = 480/3  =  160

so required value of x is 160