Find x such that 7-8 3- 7-8 5 - 7-8 x

( 7 / 8 )^ 3 ×( 7 / 8 )^ 5 =( 7 / 8 )^ 3+5 =( 7 / 8 )^ 2 =( 7 / 8 )^ x #160; ∴ x=2 ...

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Standard XII

Mathematics

Integration by Partial Fractions

Find x such...

Question

Find $x$ such that ${(\frac{7}{8})}^{3} \times {(\frac{7}{8})}^{5} = {(\frac{7}{8})}^{x}$

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Solution

${(\frac{7}{8})}^{- 3} \times {(\frac{7}{8})}^{5} = {(\frac{7}{8})}^{- 3 + 5} = {(\frac{7}{8})}^{2} = {(\frac{7}{8})}^{x}$
$∴ x = 2$

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8 x + 7 = 0

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Find x such that (78)3×(78)5=(78)x

(78)−3×(78)5=(78)−3+5=(78)2=(78)x ∴x=2

Find $x$ such that ${(\frac{7}{8})}^{3} \times {(\frac{7}{8})}^{5} = {(\frac{7}{8})}^{x}$

${(\frac{7}{8})}^{- 3} \times {(\frac{7}{8})}^{5} = {(\frac{7}{8})}^{- 3 + 5} = {(\frac{7}{8})}^{2} = {(\frac{7}{8})}^{x}$
$∴ x = 2$