log-125-ln10-log-5-e-help-me-

Question Number 100832 by student work last updated on 28/Jun/20

\log \sqrt{125} \cdot \ln 10 \cdot \log_{5} e = ?

help me

Commented by student work last updated on 28/Jun/20

what is the practice sir ?

Commented by student work last updated on 28/Jun/20

thanks sir

Commented by Dwaipayan Shikari last updated on 29/Jun/20

\frac{3}{2} l n 10

B u t i f t h e b a s e i s 10 t h e n \frac{3}{2} {l o g}_{10} 10 = \frac{3}{2}

Answered by 1549442205 last updated on 29/Jun/20

Applying the property of logarithm :

\log_{a} b \times \log_{b} c = \log_{a} c we have :

{Log}_{5} e \times \ln 10 . \log \sqrt{125} = \log_{5} 10 \times \log_{10} \sqrt{125}

\log_{5} \sqrt{125} = \log_{5} 5^{\frac{3}{2}} = \frac{3}{2}

Result equal to \frac{3}{2}

If \log \sqrt{125} {isn}^{'} t base 10 then equal to

\log_{5} 10 \times \log \sqrt{125} = \frac{3}{2} \log_{5} 10 \times \log 5 =

\frac{3}{2} \log_{x} 5 \times \log_{5} 10 = \frac{3}{2} \log_{x} 10

Commented by Dwaipayan Shikari last updated on 28/Jun/20

S i r t h e b a s e i s n o t 10