Which is the correct option?

Algebra Level 2

Which of the following equations is not correct?

log ⁡ 10 ( 2 + 3 ) = log ⁡ 10 ( 2 × 3 ) \log_{10} (2+ 3) = \log_{10}(2\times3) log ⁡ 10 1 = 0 \log_{10} 1 = 0 log ⁡ 10 ( 1 + 2 + 3 ) = log ⁡ 10 1 + log ⁡ 10 2 + log ⁡ 10 3 \log_{10} (1+2+3) = \log_{10} 1 + \log_{10}2 + \log_{10}3 log ⁡ 10 10 = 1 \log_{10} 10 = 1

Abhyudaya Apoorva by Abhyudaya Apoorva , 27, India

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2 solutions

(a) Since l o g a a = 1 log_a a = 1 , so log10 = 1.
(b) log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3
log (2 + 3) log (2 x 3)
(c) Since l o g a 1 log_a 1 = 0, so log 1 = 0.
(d) log (1 + 2 + 3) = log 6 = log (1 x 2 x 3) = log 1 + log 2 + log 3
So, (b) is incorrect.

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Sahar Bano
Mar 13, 2020

Second and fourth are correct equation due to logarithmic identities

Third, Log(1+2+3)=log(6) And log(1)+log(2)+log(3)=log(1 2 3)=log(6)

Therefore, log(1+2+3)=log(1)+log(2)+log(3)

The first is wrong as log(5)≠log(6)

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