DXC Technology Logarithms Questions and Answers Quiz-1

Solution: Take 8^x-1 common from the eq.
It reduce to
8^x-1(8² – 1) = 63
8^x-1 = 1
Hence, x – 1 = 0
x = 1

Solution: log_0.25x = 16
It can be write as
x = (0.25)¹⁶
x = (1/4)¹⁶
x = 4^-16

It can be written as
log₁₂(12³) x log₉(9⁴)
= 3log₁₂12 x 4log₉9
= 3 x 4 = 12

Solution: It can be write as
log_x(3 x 9 x 27 x 81) = 10
log_x(3¹ x 3² x 3³ x 3⁴) = 10
log_x(3¹⁰) = 10
10 log_x3 = 10
then, x = 3

Solution: log₁₀((a + 3)(a – 3))=1
log₁₀(a² – 9) = 1
(a² – 9) = 10
a² = 19
a = √19

log_abcd(ab) + log_abcd(bc) + log_abcd(cd) + log_abcd(da)
=log_abcd(ab * bc * cd * da)
=log_abcd(abcd)²
=2 log_abcd(abcd)
=2

log(xⁿ yⁿ / zⁿ * yⁿ zⁿ / xⁿ * zⁿ xⁿ / yⁿ)
= log xⁿ yⁿ zⁿ
= log(xyz)ⁿ
= log₁₀ 10ⁿ
= n

Apply logarithm on both sides
log_(121/10)(121/10)^x = log_(121/10)3
x = (log 3) / (log 121 – log 10)
x = (log 3) / (2 log 11 – 1)

log(2x² + 17)= log (x² – 6x + 9)
2x² + 17 = x² – 6x + 9
x² + 6x + 8 = 0
x² + 4x + 2x + 8 = 0
x(x + 4) + 2(x + 4) = 0
(x + 4)(x + 2)=0
x= -4,-2

Put x = 0
log₂(33 – 1)= 10^log(5)
log₂32 = 5
5 log₂ 2 = 5
5 = 5
LHS = RHS