Question

answer this question

Answer 1

We know that

=> a^m × a^n = a^(m+n)

=> a^(-m) = 1/a^m

=> a^m = a^n
then m = n
=> a^m / a^n = a^(m-n)

1) (5/3)^(-2) × (5/3)^(-14) = (5/3)^8x

(5/3)^( -2 + (-14)) = (5/3)^8x

(5/3)^( -2 -14)) = (5/3)^8x

(5/3)^( -16 ) = (5/3)^8x

bases are equal..so equate the powers..

-16 = 8x

-16/8 = x

-2 = x is the answer

2) (-2)^3 × (-2)^(-6) = -2^(2x-1)

(-2)^3 × 1/ (-2)^6 = -2^(2x-1)

(-2)^3/(-2)^6= -2^(2x-1)

(-2)^(3-6)= -2^(2x-1)

(-2)^(-3) = -2^(2x-1)

bases are equal so equate the powers

-3 = 2x -1

-3 +1 = 2x

-2 = 2x

-2/2 = x

-1 = x is the answer...


3) (2^(-1) + 4^(-1) +6^(-1) +8^(-1))^x = 1

(1/2 + 1/4 + 1/6 +1/8)^x = 1

LCM ..2,4,6,8 = 24

(1(12) + 1(6) + 1(4) + 1(3) / 24))^x = 1

( (25/24)^x = 1

Taking (log), we get

x log(25/24) = log(1)

x log(25/24) = 0

x = 0