Log-105 - log-108 - 2log-102 -4log-1021

The correct option is C 1Given log_105 + log_108 2log_102 [We know nbsp;log_am + log_an = log_amn] = log_105× 8 2log_102 [As log_an^m=m log_an] = log_105 ...

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Byju's Answer

Standard X

Mathematics

Properties of Logarithms

log_105 + log...

Question

${log}_{10} 5 + {log}_{10} 8 - 2 {log}_{10} 2$ =

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{log}_{10} 2

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Solution

The correct option is C 1
Given ${log}_{10} 5 + {log}_{10} 8 - 2 {log}_{10} 2$
[We know ${log}_{a} m + l o g_{a} n = l o g_{a} m n$ ]
= ${log}_{10} 5 \times 8 - 2 {log}_{10} 2$
[As $l o g_{a} n^{m} = m l o g_{a} n$ ]
= ${log}_{10} 5 \times 8 - {log}_{10} 4$
[Also ${log}_{a} \frac{m}{n} = l o g_{a} m - l o g_{a} n$ ]
= ${log}_{10} \frac{40}{4}$
= ${log}_{10} 10 = 1$

Suggest Corrections

log105+log108−2log102 =

The correct option is C 1Given log105+log108−2log102 [We know logam+logan=logamn] = log105×8−2log102 [As loganm=m logan] = log105×8−log104 [Also logamn=logam−logan] = log10404 = log1010=1

${log}_{10} 5 + {log}_{10} 8 - 2 {log}_{10} 2$ =