If log8p=25and log2q=5,then - If log8p=25and log2q=5,then - {\text{If }}\,\,{\text{lo}}{{\text{g}}_8}{\text{p}} = 25\,\,{\text{and lo}}{{\text{g}}_2}{\text{q}} = 5\,,{\text{then - }}" /> If log8p=25and log2q=5,then - If log8p=25and log2q=5,then - {\text{If }}\,\,{\text{lo}}{{\text{g}}_8}{\text{p}} = 25\,\,{\text{and lo}}{{\text{g}}_2}{\text{q}} = 5\,,{\text{then - }}" /> If log8p=25and log2q=5,then - If log8p=25and log2q=5,then - {\text{If }}\,\,{\text{lo}}{{\text{g}}_8}{\text{p}} = 25\,\,{\text{and lo}}{{\text{g}}_2}{\text{q}} = 5\,,{\text{then - }}" />

India’s No.1 Educational Platform For UPSC,PSC And All Competitive Exam

Download Our App

$If lo g_{8} p = 25 and lo g_{2} q = 5, then -$ ${\text{If }}\,\,{\text{lo}}{{\text{g}}_8}{\text{p}} = 25\,\,{\text{and lo}}{{\text{g}}_2}{\text{q}} = 5\,,{\text{then - }}$

1p = q¹⁵
2p² = q³
3p = q⁵
4p³ = q

Answer:- 1

Explanation:-

Solution:

\begin{aligned} lo g_{8} p = 25 and lo g_{2} q = 5 \\ \Rightarrow p  = 8^{25} and q = 2^{5} \\ \Rightarrow p  = {(2^{3})}^{25} and q  = 2^{5} \\ \Rightarrow p  = 2^{75} and q  = 2^{5} \\ \Rightarrow p  = {(2^{5})}^{15} and q  = 2^{5} \\ \Rightarrow p  = q^{15} \end{aligned}

$\eqalign{ & {\text{lo}}{{\text{g}}_8}{\text{p}} = 25\,\,{\text{and lo}}{{\text{g}}_2}{\text{q}} = 5\, \cr & \Rightarrow {\text{p = }}{{\text{8}}^{25}}\,{\text{and q}} = {2^5} \cr & \Rightarrow {\text{p = }}{\left( {{2^3}} \right)^{25}}{\text{ and q = }}{2^5} \cr & \Rightarrow {\text{p = }}{{\text{2}}^{75}}{\text{ and q = }}{2^5} \cr & \Rightarrow {\text{p = }}{\left( {{2^5}} \right)^{15}}{\text{ and q = }}{2^5} \cr & \Rightarrow {\text{ p = }}{{\text{q}}^{15}} \cr}$

Workspace Report

Post your Comments

", "text": "

If lo g_{8} p = 25 and lo g_{2} q = 5, then -

${\text{If }}\,\,{\text{lo}}{{\text{g}}_8}{\text{p}} = 25\,\,{\text{and lo}}{{\text{g}}_2}{\text{q}} = 5\,,{\text{then - }}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} lo g_{8} p = 25 and lo g_{2} q = 5 \\ \Rightarrow p  = 8^{25} and q = 2^{5} \\ \Rightarrow p  = {(2^{3})}^{25} and q  = 2^{5} \\ \Rightarrow p  = 2^{75} and q  = 2^{5} \\ \Rightarrow p  = {(2^{5})}^{15} and q  = 2^{5} \\ \Rightarrow p  = q^{15} \end{aligned}

$\eqalign{ & {\text{lo}}{{\text{g}}_8}{\text{p}} = 25\,\,{\text{and lo}}{{\text{g}}_2}{\text{q}} = 5\, \cr & \Rightarrow {\text{p = }}{{\text{8}}^{25}}\,{\text{and q}} = {2^5} \cr & \Rightarrow {\text{p = }}{\left( {{2^3}} \right)^{25}}{\text{ and q = }}{2^5} \cr & \Rightarrow {\text{p = }}{{\text{2}}^{75}}{\text{ and q = }}{2^5} \cr & \Rightarrow {\text{p = }}{\left( {{2^5}} \right)^{15}}{\text{ and q = }}{2^5} \cr & \Rightarrow {\text{ p = }}{{\text{q}}^{15}} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} lo g_{8} p = 25 and lo g_{2} q = 5 \\ \Rightarrow p  = 8^{25} and q = 2^{5} \\ \Rightarrow p  = {(2^{3})}^{25} and q  = 2^{5} \\ \Rightarrow p  = 2^{75} and q  = 2^{5} \\ \Rightarrow p  = {(2^{5})}^{15} and q  = 2^{5} \\ \Rightarrow p  = q^{15} \end{aligned}

$\eqalign{ & {\text{lo}}{{\text{g}}_8}{\text{p}} = 25\,\,{\text{and lo}}{{\text{g}}_2}{\text{q}} = 5\, \cr & \Rightarrow {\text{p = }}{{\text{8}}^{25}}\,{\text{and q}} = {2^5} \cr & \Rightarrow {\text{p = }}{\left( {{2^3}} \right)^{25}}{\text{ and q = }}{2^5} \cr & \Rightarrow {\text{p = }}{{\text{2}}^{75}}{\text{ and q = }}{2^5} \cr & \Rightarrow {\text{p = }}{\left( {{2^5}} \right)^{15}}{\text{ and q = }}{2^5} \cr & \Rightarrow {\text{ p = }}{{\text{q}}^{15}} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

Test

Classes

E-Book