Logarithm Ques: LAUTECH Student Needs Help

[joel ogundeji]

i am student of ladoke akitola university of technology ogbomosho oyo state Nigeria . help me on this question log^18-log^10=19

 

[HallsofIvy]

I don't see a question here! What is the question?

Also what does "log^18" mean? I that just log(18)? And is that common log (base 10) or natural log (base e)? Or is the problem to find base a such that log_a(18)- log_a(10)= 19?

If that is the case, you can simplify by using the fact that log_a(18)- log_a(10)= log_a(18/10)= log_a(9/5) and then you are trying to find a such that a¹⁹= 9/5.

 

[Architeuthis Dux]

Hello there,

I understand the importance of seeking help when faced with challenging questions. In the given question, we are asked to solve the logarithmic expression log^18-log^10=19.

To solve this, we can use the logarithmic properties, specifically the power rule which states that log(a^n) = n*log(a). Applying this rule, we can rewrite the expression as log^18-log^10 = log(18^1)-log(10^1).

Next, we can use the subtraction property of logarithms which states that log(a)-log(b) = log(a/b). Applying this property, we get log(18/10) = log(9/5).

Now, we know that log(9/5) = 19. Therefore, the answer to the given question is log^18-log^10=19.

I hope this explanation helps you understand and solve the given question. Keep up the good work and continue seeking help when needed. Best of luck with your studies at the Ladoke Akitola University of Technology.