Find the value of p29p-2923-2977

Find the value of pGiven (29)^p÷(29)^23=(29)^77 ⇒(29)^77=29^p/29^230ex0ex⇒(29)^77×(29)^23 =29^p0ex0ex⇒29^P = (29)^77×(29)^230ex0ex⇒29^P=(29)^77+23Compar ...

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Standard IX

Mathematics

Property 3

Find the valu...

Question

Find the value of $p$
${(29)}^{p} \div {(29)}^{23} = {(29)}^{77}$

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Solution

Find the value of $p$
Given ${(29)}^{p} \div {(29)}^{23} = {(29)}^{77}$
$\Rightarrow {(29)}^{77} = \frac{29^{p}}{29^{23}} \Rightarrow {(29)}^{77} \times {(29)}^{23} = 29^{p} \Rightarrow 29^{P} = {(29)}^{77} \times {(29)}^{23} \Rightarrow 29^{P} = {(29)}^{77 + 23}$
Comparing the base and power of above expression
$p = 77 + 23 \Rightarrow 100$
Hence, the value of $p$ is $100 .$

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Find the value of p29p÷2923=2977

Find the value of pGiven 29p÷2923=2977 ⇒2977=29p2923⇒2977×2923=29p⇒29P=2977×2923⇒29P=2977+23Comparing the base and power of above expression p=77+23⇒100Hence, the value of p is 100.

Find the value of $p$
${(29)}^{p} \div {(29)}^{23} = {(29)}^{77}$