# Thread: product of two logs -proof without word

1. ## product of two logs -proof without word

Dear Sir,

I have an interesting problem and hope you can shed some light on it
I wonder whether you have encountered any simpler proof which comes with a geometrical interpretation of the below theorem .(or proof without words)
thanks
kingman
.
loga to the base b times logb to the base a equals 1

2. Originally Posted by kingman
Dear Sir,

I have an interesting problem and hope you can shed some light on it
I wonder whether you have encountered any simpler proof which comes with a geometrical interpretation of the below theorem .(or proof without words)
thanks
kingman
.
loga to the base b times logb to the base a equals 1
\log_b{a}\time\log_a{b}

\frac{log(a)}{log(b)}*\frac{log(b)}{log(a)}

3. [quote=sa-ri-ga-ma;510604]
$\displaystyle \log_b{a}\time\log_a{b}$

$\displaystyle \frac{log(a)}{log(b)}*\frac{log(b)}{log(a)}$

4. ## Thanks but...

Dear sa-ri-ga-ma,
Thanks for algebraic approach to the problem and what
the question is looking for is the geometrical interpretation .
.
thanks
kingman

5. ## 'Proof Without Words '

Dear sa-ri-ga-ma,
Thanks for algebraic approach to the problem and I can understand how to prove it algebraically but what
the question is looking for is a geometrical proof for it. This is similar to asking for 'Proof Without Words 'type of answer.
.
Thanks
kingman