CrazySnowGirL
Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

[tex]{x}^{18}={y}^{21}={z}^{28}[/tex]
3, [tex]3 log_y x [/tex], [tex]3 log_z y [/tex] and [tex]7 log_x z [/tex] are in?​

Sagot :

[tex]\large\bold{\underline{\underline{Question:-}}}[/tex]

[tex]{x}^{18}={y}^{21}={z}^{28}[/tex]

3, [tex]3 log_y x [/tex], [tex]3 log_z y [/tex] and [tex]7 log_x z [/tex] are in??

[tex]\large\bold{\underline{\underline{Answer:-}}}[/tex]

The Series in AP.

[tex]\large\bold{\underline{\underline{Explanation:-}}}[/tex]

[tex]{x}^{18}={y}^{21}={z}^{28} [/tex]

[tex]{x}^{18}={y}^{21}[/tex]

By taking LOG on both sides

[tex]log {x}^{18}=log {y}^{21} [/tex]

[tex]18 log x= 21 log y[/tex]

[tex]2 \ times 3 log x= 7 log y[/tex]

[tex] 3 \dfrac{log x}{log y} =\dfrac{7}{2}[/tex]

[tex]\bold{ 3 log_y x =\dfrac{7}{2}}[/tex]

Now,

[tex]{x}^{18}={z}^{28} [/tex]

By taking LOG on both sides

[tex]log {x}^{18}=log {z}^{28} [/tex]

[tex]18 log x =28 log z [/tex]

[tex] 9 log x =7 \times 2 log z [/tex]

[tex] 7\dfrac{log z}{log x} = \dfrac{9}{2}[/tex]

[tex]\bold{7 log_x z= \dfrac{9}{2}}[/tex]

Now,

[tex]{y}^{21}={z}^{28} [/tex]

By taking LOG on both sides

[tex]log {y}^{21}=log {z}^{28} [/tex]

[tex]21 log y=28 log z [/tex]

[tex] 3 log y = 4 log z [/tex]

[tex]3 \dfrac{ log y}{logz }= 4 [/tex]

[tex]\bold{ 3 log_z y = 4 }[/tex]

According to the question:-

3, [tex]3 log_y x [/tex], [tex]3 log_z y [/tex] and [tex]7 log_x z [/tex] are ...in??

we have,

[tex]\bold{ 3 log_y x =\dfrac{7}{2}}[/tex]

[tex]\bold{7 log_x z= \dfrac{9}{2}}[/tex]

[tex]\bold{ 3 log_z y = 4 }[/tex]

The series is,

[tex]3 , \: \dfrac{7}{2 } , \: 4 , \: \dfrac{9}{2}[/tex]

Here,

[tex]a_1 = 3 [/tex]

[tex]a_2 = \dfrac{7}{2 } [/tex]

[tex]a_3 = 4 [/tex]

[tex]a_2 = \dfrac{7}{2 } [/tex]

Let, us find common difference

[tex]d \implies a_2 - a_1 = = a_3-a_2 [/tex]

[tex]d \implies 2 a_2 = a_3+a_1 [/tex]

[tex]d \implies 2 \times \dfrac{7}{2}= 7 [/tex]

[tex]d \implies 7 = 7 [/tex]

Since, common difference is equal!

The series is in AP.

We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.