Write 4log 4+2log 5log 15 As A Single Logarithm Class 10 Maths CBSE

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AnswerQuestion Answers for Class 12Class 12 BiologyClass 12 ChemistryClass 12 EnglishClass 12 MathsClass 12 PhysicsClass 12 Social ScienceClass 12 Business StudiesClass 12 EconomicsQuestion Answers for Class 11Class 11 EconomicsClass 11 Computer ScienceClass 11 BiologyClass 11 ChemistryClass 11 EnglishClass 11 MathsClass 11 PhysicsClass 11 Social ScienceClass 11 AccountancyClass 11 Business StudiesQuestion Answers for Class 10Class 10 ScienceClass 10 EnglishClass 10 MathsClass 10 Social ScienceClass 10 General KnowledgeQuestion Answers for Class 9Class 9 General KnowledgeClass 9 ScienceClass 9 EnglishClass 9 MathsClass 9 Social ScienceQuestion Answers for Class 8Class 8 ScienceClass 8 EnglishClass 8 MathsClass 8 Social ScienceQuestion Answers for Class 7Class 7 ScienceClass 7 EnglishClass 7 MathsClass 7 Social ScienceQuestion Answers for Class 6Class 6 ScienceClass 6 EnglishClass 6 MathsClass 6 Social ScienceQuestion Answers for Class 5Class 5 ScienceClass 5 EnglishClass 5 MathsClass 5 Social ScienceQuestion Answers for Class 4Class 4 ScienceClass 4 EnglishClass 4 MathsWrite $4\log 4+2\log 5-\log 15$ as a single logarithm.AnswerVerified598.2k+ viewsHint: We will use some basic forms of logarithm like to write the given logarithm into a single term logarithm as $a\log b$ can be written as $\log ({{b}^{a}})$, and $\log a+\log b$ can be written as $\log (ab)$, and $\log a-\log b$ can be written as $\log \dfrac{a}{b}$.Complete step-by-step answer:We have given the logarithm equation as $4\log 4+2\log 5-\log 15$ and we have to write it in a single logarithm form. We know that $a\log b$ can be written as $\log ({{b}^{a}})$, and $\log a+\log b$ can be written as $\log (ab)$, and $\log a-\log b$ can be written as $\log \dfrac{a}{b}$. We will use these three basic formulas of logarithm to write the given expression of logarithm into a single logarithm. So, we can write $4\log 4$ as $\log ({{4}^{4}})$ and we can write$2\log 5$ as $\log ({{5}^{2}})$. Therefore $\log ({{4}^{4}})=log256$ and $\log ({{5}^{2}})=log25$.So, we get logarithm expression as = $\log 256+\log 25-\log 15$, Therefore applying the rule $\log a+\log b$ can be written as $\log (ab)$, we get the modified equation as = \[log\text{ }\left( 256x25 \right)\text{ }-\text{ }log\text{ }15\], now we apply the rule $\log a-\log b$ can be written as $\log \dfrac{a}{b}$ to get modified equation as = $\log \left( \dfrac{\left( 256\times 25 \right)}{15} \right)$ = $\log \left( \dfrac{6400}{15} \right)$ = $\log \left( \dfrac{1280}{3} \right)$ Therefore, given the expression $4\log 4+2\log 5-\log 15$ can be written as $\log \left( \dfrac{1280}{3} \right)$.Note: Using direct logarithmic formula to reduce any logarithmic function will reduce our effort. Logarithmic functions are very helpful for calculating tedious math equations that we cannot calculate with normal mathematical steps. Only care one has to take is of the logarithmic bases. It can be exponential or base 10. Antilogarithm is also a concept that goes hand in hand with logarithm. If we do not use direct formula of logarithm like $a\log b$ can be written as $\log ({{b}^{a}})$, $\log a+\log b$ can be written as $\log (ab)$, then the chances of error in our solution will be increased and also, we have to add unnecessary lines which will consume our time.Recently Updated PagesMaster Class 12 Business Studies: Engaging Questions & Answers for SuccessMaster Class 12 Economics: Engaging Questions & Answers for SuccessMaster Class 12 English: Engaging Questions & Answers for SuccessMaster Class 12 Maths: Engaging Questions & Answers for SuccessMaster Class 12 Social Science: Engaging Questions & Answers for SuccessMaster Class 12 Chemistry: Engaging Questions & Answers for SuccessMaster Class 12 Business Studies: Engaging Questions & Answers for SuccessMaster Class 12 Economics: Engaging Questions & Answers for SuccessMaster Class 12 English: Engaging Questions & Answers for SuccessMaster Class 12 Maths: Engaging Questions & Answers for SuccessMaster Class 12 Social Science: Engaging Questions & Answers for SuccessMaster Class 12 Chemistry: Engaging Questions & Answers for Success

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