Basic Conversion of Logarithm

Algebra Level 2

If log ⁡ p 5 = a \log_p 5 = a , then express log ⁡ p p 5 × log ⁡ 5 p \log_p \dfrac {p} {5} \times \log_5 p in terms of a a .

1 − 1 a 1- \frac1a 1 a − 1 \frac1a - 1

Manimegalai Ganesamurthy by Manimegalai Ganesamurthy , 21, Canada

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Pham Khanh
Apr 23, 2016

log ⁡ p 5 = a \log_{p}{5}=a ⟹ log ⁡ 5 p = 1 a \implies \log_{5}{p}=\frac{1}{a} So log ⁡ p p 5 × log ⁡ 5 p \log_{p}{\frac{p}{5}} \times \log_{5}{p} = ( log ⁡ p p − l o g p 5 ) × log ⁡ 5 p =(\log_{p}{p}-log_{p}{5}) \times \log_{5}{p} = ( 1 − a ) × 1 a = 1 a − 1 =(1-a) \times \frac{1}{a}=\color{#D61F06}{\frac{1}{a}-1} Hence, the answer is 1 a − 1 \LARGE \color{#20A900}{\boxed{\color{#D61F06}{\frac{1}{a}-1}}}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...