{"id":387,"date":"2022-04-13T09:13:58","date_gmt":"2022-04-13T09:13:58","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=387"},"modified":"2024-01-05T09:03:44","modified_gmt":"2024-01-05T09:03:44","slug":"w-7-power-property-of-logarithms","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/w-7-power-property-of-logarithms\/","title":{"rendered":"W.7 Power property of logarithms"},"content":{"rendered":"\n

Power property of logarithms<\/strong><\/h2>\n\n\n\n

key notes:<\/p>\n\n\n\n

Product Property: <\/strong>logb<\/sub> M + logb<\/sub> N = logb<\/sub> MN, where b, M, and N are positive, and b\u22601.<\/p>\n\n\n\n

Quotient Property: <\/strong>logb<\/sub> M \u2013 logb<\/sub> N = logb<\/sub> M\/N , where b, M, and N are positive, and b\u22601.<\/p>\n\n\n\n

Power Property: <\/strong>logb<\/sub> MN<\/sup> = N logb <\/sub>M, where b and M are positive, and b\u22601.<\/p>\n\n\n\n

A\u00a0common logarithm<\/strong>\u00a0uses base 10. The common logarithm\u00a0log10<\/sub> x\u00a0is usually written as\u00a0logx,\u00a0without the\u00a0base.<\/p>\n\n\n\n

Learn with an example<\/strong><\/p>\n\n\n\n

\n
\n

\u27a1\ufe0f Expand the logarithm. Assume all expressions exist and are well-defined.<\/p>\n\n\n\n

Write\u00a0your answer as a sum or difference of common logarithms or multiples of common logarithms.<\/p>\n\n\n\n

The inside of each logarithm must be a distinct constant or\u00a0variable.<\/p>\n\n\n\n

log x2<\/sup><\/p>\n\n\n\n

_______<\/p>\n<\/div><\/div>\n\n\n\n

Expand the logarithm. <\/p>\n\n\n\n

log x2<\/sup><\/p>\n\n\n\n

= 2 log x Power Property<\/p>\n\n\n\n

You could also use the Product Property.<\/p>\n\n\n\n

log x2<\/sup><\/p>\n\n\n\n

= log (x . x) Definition of exponent<\/p>\n\n\n\n

= log x + log x Product Property<\/p>\n\n\n\n

= 2 log x Combine like terms<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

\u27a1\ufe0f Expand the logarithm. Assume all expressions exist and are well-defined.<\/p>\n\n\n\n

Write\u00a0your answer as a sum or difference of common logarithms or multiples of common logarithms. <\/p>\n\n\n\n

The inside of each logarithm must be a distinct constant or\u00a0variable.<\/p>\n\n\n\n

log v9<\/sup><\/p>\n\n\n\n

_______<\/p>\n<\/div><\/div>\n\n\n\n

Expand the logarithm. <\/p>\n\n\n\n

log v9<\/sup><\/p>\n\n\n\n

= 9 log v Power Property<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

\u27a1\ufe0f Expand the logarithm. Assume all expressions exist and are well-defined.<\/p>\n\n\n\n

Write\u00a0your answer as a sum or difference of common logarithms or multiples of common logarithms. <\/p>\n\n\n\n

The inside of each logarithm must be a distinct constant or\u00a0variable.<\/p>\n\n\n\n

log r2<\/sup><\/p>\n\n\n\n

_______<\/p>\n<\/div><\/div>\n\n\n\n

Expand the logarithm. <\/p>\n\n\n\n

log r2<\/sup><\/p>\n\n\n\n

= log (r . r) Definition of exponent<\/p>\n\n\n\n

= log r + log r Product Property<\/p>\n\n\n\n

= 2 log r Combine like terms<\/p>\n<\/div><\/div>\n\n\n\n

let’s practice!<\/p>\n\n\n\n

\n
\n
\"\"<\/figure>\n<\/div>\n\n\n\n
\n
\"\"<\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Power property of logarithms key notes: Product Property: logb M + logb N = logb MN, where b, M, and N are positive, and b\u22601. Quotient Property: logb M \u2013 logb N = logb M\/N , where b, M, and N are positive, and b\u22601. Power Property: logb MN = N logb M, where b and M are positive, and b\u22601. A\u00a0common logarithm\u00a0uses base 10. The common logarithm\u00a0log10 x\u00a0is usually written as\u00a0logx,\u00a0without the\u00a0base. Learn with an example \u27a1\ufe0f Expand the logarithm. AssumeContinue reading “W.7 Power property of logarithms”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-387","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/387","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=387"}],"version-history":[{"count":8,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/387\/revisions"}],"predecessor-version":[{"id":12058,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/387\/revisions\/12058"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=387"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}