Question

In the equation frac{{{7^{48}} - {7^{47}} - {7^{46}}}}{{41}},, = ,{7^x} , what is the value of x?
(1)
48
(2)
47
(3)
49
(4)
46​

Answer 1

Qᴜᴇsᴛɪᴏɴ :-

$\bf \: \dfrac{({7}^{48} -{7}^{47} -{7}^{46})}{41} = {7}^{x}\\\\\bf \: find \: x \: .$

Sᴏʟᴜᴛɪᴏɴ :-

$\red\longmapsto\:\rm \:\dfrac{({7}^{48} -{7}^{47} -{7}^{46})}{41} = {7}^{x}\\\\ \bf \: taking \: common \\ \\\red\longmapsto\:\rm \:\dfrac{ {7}^{46} ({7}^{2} -{7}^{1} -1)}{41} = {7}^{x}\\\\ \red\longmapsto\:\rm \:\dfrac{{7}^{46} (49 -7 -1)}{41}={7}^{x}\\\\ \red\longmapsto\:\rm \:\dfrac{ {7}^{46} \cancel{(41)}}{ \cancel{41}} = {7}^{x}\\\\ \red\longmapsto\:\rm \: {7}^{46} = {7}^{x}\\\\\red\longmapsto\:\rm \:\bold{\boxed{\large{\boxed{\orange{\small{\boxed{\large{\red{\bold{x = 46}}}}}}}}}}$

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Answer 2

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

$\dagger \: {\sf{ \frac{ {7}^{48} - {7}^{47} - {7}^{46} }{41} = {7}^{x} }}$

${\bf{\blue{\underline{To\:Find:}}}}$

• Value of x.

${\bf{\blue{\underline{Now:}}}}$

$: \implies {\sf{ \frac{ {7}^{48} - {7}^{47} - {7}^{46} }{41} = {7}^{x} }}$

$: \implies {\sf{ \frac{ {7}^{46} ({7}^{2} - {7}^{1} - 1 ) }{41} = {7}^{x} }}$

$: \implies {\sf{ \frac{ {7}^{46} (49 - 7 - 1 ) }{41} = {7}^{x} }}$

$: \implies {\sf{ \frac{ {7}^{46} (41 ) }{41} = {7}^{x} }}$

$: \implies {\sf{ \frac{ {7}^{46} ( \cancel{41 }) }{ \cancel{41}} = {7}^{x} }}$

$: \implies{\sf{ {7}^{46} = {7}^{x} }}$

If bases are equal exponent will also be equal,

$: \implies{\sf{ x = 46}}$