Explore topic-wise InterviewSolutions in .

log 2⁵⁶ =56log2=(56*0.30103)=16.85768. 

Its characteristics is 16. 

Hence,the number of digits in 2⁵⁶ is 17.

log₁₀ 50=log₁₀ (100/2)=log₁₀ 100-log₁₀ 2=2-0.30103=1.69897.

log₁₀ 3+log₁₀ (4x+1)=log₁₀ (x+1)+1 

Log₁₀ 3+log₁₀ (4x+1)=log₁₀ (x+1)+log₁₀ (x+1)+log₁₀ 10 

Log₁₀ (3(4x+1))=log₁₀ (10(x+1)) 

=3(4x+1)=10(x+1)=12x+3 

=10x+10 

=2x=7

x=7/2

Given expression: log_xyz xy+ log_xyz yz+ log_xyz zx 

= log_xyz (xy*yz*zx)=log_xyz (xyz)² 

2log_xyz(xyz)=2*1=2

3 log₈x = log₄ (x+6)

⇒ 3 log_2³x = log_2² (x+6) (∵ log_a^mb = 1/m log_ab)

⇒ 3/3 log₂x = 1/2 log₂ (x+6)

⇒ 2 log₂x = log₂ (x+6)

⇒ log₂x² = log₂ (x+6)  (∵ n log a = log aⁿ)

⇒ x² = x+6  (By taking anti log)

⇒ x² - x - 6 = 0

⇒ x² - 3x + 2x - 6 = 0

⇒ x(x-3) + 2(x-3) = 0

⇒ (x+2) (x-3) = 0

⇒ x+2 = 0 or x-3 = 0

⇒ x = -2(Not possible) or x = 3)

(∵ Domain of log x is x > 0)

Hence, solution is x = 3

We know that log_a a=1,so log₃₄ 34=0. 

Let log₃ 27=3³ or n=3. 

ie, log₃ 27 = 3.