Iflog10a=p,log10b=q,thenwhatislog10(apbq)equalto?Iflog10a=p,log10b=q,thenwhatislog10(apbq)equalto?\eqalign{ & {\text{If}}\,{\log _{10}}a = p,\,\,\,{\log _{10}}b = q, \cr & {\text{then}}\,{\text{what}}\,\,{\text{is}}\,\,{\log _{10}}\left( {{a^p}{b^q}} \right)\,\,{\text{equal}}\,\,{\text{to}}? \cr} " /> Iflog10a=p,log10b=q,thenwhatislog10(apbq)equalto?Iflog10a=p,log10b=q,thenwhatislog10(apbq)equalto?\eqalign{ & {\text{If}}\,{\log _{10}}a = p,\,\,\,{\log _{10}}b = q, \cr & {\text{then}}\,{\text{what}}\,\,{\text{is}}\,\,{\log _{10}}\left( {{a^p}{b^q}} \right)\,\,{\text{equal}}\,\,{\text{to}}? \cr} " /> Iflog10a=p,log10b=q,thenwhatislog10(apbq)equalto?Iflog10a=p,log10b=q,thenwhatislog10(apbq)equalto?\eqalign{ & {\text{If}}\,{\log _{10}}a = p,\,\,\,{\log _{10}}b = q, \cr & {\text{then}}\,{\text{what}}\,\,{\text{is}}\,\,{\log _{10}}\left( {{a^p}{b^q}} \right)\,\,{\text{equal}}\,\,{\text{to}}? \cr} " />

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$\begin{aligned} If \log_{10} a = p, \log_{10} b = q, \\ then what is \log_{10} (a^{p} b^{q}) equal to ? \end{aligned}$ $\eqalign{ & {\text{If}}\,{\log _{10}}a = p,\,\,\,{\log _{10}}b = q, \cr & {\text{then}}\,{\text{what}}\,\,{\text{is}}\,\,{\log _{10}}\left( {{a^p}{b^q}} \right)\,\,{\text{equal}}\,\,{\text{to}}? \cr}$

1p² + q²
2p² - q²
3p²q²
4^p²/_q²

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Given, \\ \log_{10} a = p, \log_{10} b = q \\ \log_{10} (a^{p} b^{q}) = \log_{10} a^{p} + \log_{10} b^{q} \\ = p \log_{10} a + q \log_{10} b \\ = p^{2} + q^{2} \end{aligned}

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", "text": "

\begin{aligned} If \log_{10} a = p, \log_{10} b = q, \\ then what is \log_{10} (a^{p} b^{q}) equal to ? \end{aligned}

$\eqalign{ & {\text{If}}\,{\log _{10}}a = p,\,\,\,{\log _{10}}b = q, \cr & {\text{then}}\,{\text{what}}\,\,{\text{is}}\,\,{\log _{10}}\left( {{a^p}{b^q}} \right)\,\,{\text{equal}}\,\,{\text{to}}? \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} Given, \\ \log_{10} a = p, \log_{10} b = q \\ \log_{10} (a^{p} b^{q}) = \log_{10} a^{p} + \log_{10} b^{q} \\ = p \log_{10} a + q \log_{10} b \\ = p^{2} + q^{2} \end{aligned}

$\eqalign{ & {\text{Given}}, \cr & {\log _{10}}a = p,\,{\log _{10}}b = q \cr & {\log _{10}}\left( {{a^p}{b^q}} \right) = {\log _{10}}{a^p} + {\log _{10}}{b^q} \cr & = p{\log _{10}}a + q{\log _{10}}b \cr & = {p^2} + {q^2} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution: