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Algebra Level 1

$\large \log5+\log10+\log2-\log100 = \ ?$

100 1 0 10

15 solutions

Felix Harvey-Rosser
Aug 13, 2015

$\begin{aligned}\log5+\log10+\log2-\log100&=\log\frac{5\times10\times2}{100}\\ &=\log1\\&=0\end{aligned}$

Naveen Kumar
Aug 9, 2015

log5+log10=log50, log50+log2=log100, log100-log100=0, and that's it

Paola Ramírez
Aug 13, 2015

By properties of logarithms

$\log A+\log B=\log AB \Rightarrow \log 5+\log2=\log10$

$\log A^n=n\log A \Rightarrow -\log 100=-\log 10^2=-2\log 10$ .

Now, rewriting we get:

$\log 10+\log10-2\log10=\boxed{0}$

Super guys

Thangavelraj Thangam - 5 years, 10 months ago

André Winston
Aug 13, 2015

could I say that log100 - log100 = log(100/100)? I'm almost sure that this property isn't valid, but could someone clarify it? because it actually solves the problem.

It's a valid property that log 100 - log 100 = log(100/100) = log 1 = 0

Addition of log with same base can be simplified as multiplication..so does the substraction of log with same base..you have to division now..

Razik Ridzuan - 5 years, 10 months ago

log(100/100)=log1=0 , I think it was like this.

Gourab Roy - 5 years, 10 months ago

My answer to you is very simple; log(100/100) actually gives you the right answer since log applies to both numbers and 100/100 obviously = 1. So you will come to the same conclusion [(log1)=(o)], however, in most cases teachers would give you half of the mark since you failed to right the correct property which is log100 - log100. I had a feelin you knew this already though. :)

Liam Bennett - 5 years, 9 months ago

Christoffer Santos
Aug 13, 2015

log 100 = (2 log 5 + 2 log 2) log 10 = (log 5 + log 2 ) 2 log 5 - log 2 - 2 log 5 + log 2 = 0

Andriane Casuga
Aug 13, 2015

Let base 10 of all. So, log5+1+log2-2 = log(5*2) -1 = 1-1 = 0 (Ans)

Hans Tananda
Aug 13, 2015

Since log a + log b= log a * b and log a - log b = log a / b, then log5 + log10 + log 2 - log100 = log(5 * 10 * 2 / 100) = log (1) = 0

Sai Ram
Aug 12, 2015

That's simple.

$\large \log5+\log10+\log2-\log100 \$

The given expression can be written as

$\large\log50+\log2-\log100= \log100-\log100=0.$

Jace Woody
Aug 26, 2015

Log is multiplying all of them together. 5x2x10 -100

محمد كذلك
Aug 26, 2015

Since log a + log b= log a * b and log a - log b = log a / b, then log5 + log10 + log 2 - log100 = log(5 * 10 * 2 / 100) = log (1) = 0

Vedant Tiwari
Aug 26, 2015

log5 + log10 + log2 = log(5x10) + log2 = log(50x2) = log100 ==>So log100 - log100 = 0

Hi dude, instead of writing your solutions like this start using $\LaTeX$ .You can check this and this (You can use this one to double check your $\LaTeX$ ).See ya later dude.