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Byju's Answer

Standard XII

Mathematics

Monotonically Increasing Functions

log 10p+log 1...

Question

${log}_{10} p + {log}_{10} q = {log}_{10} (p - q)$ then

p = q = 0

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p = \frac{q}{1 + q}

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p = q = 1

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p = \frac{q}{1 - q}

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Solution

The correct option is B $p = \frac{q}{1 - q}$
${log}_{10} p + {log}_{10} q = {log}_{10} (p - q)$
${log}_{10} p q = {log}_{10} (p - q)$
$p q = p - q$
$p (q - 1) = - q$
$p = \frac{q}{1 - q}$

Suggest Corrections

Similar questions

Q. If

P

is the number of natural numbers whose logarithms to the base

10

have the characteristic

p

and

Q

is the number of natural numbers, logarithms of whose reciprocals to the base

10

have the characteristic

- q

, then the value of

{log}_{10} P - {log}_{10} Q

Q. Let

{log}_{10} p = 0.030, {log}_{10} q = - 2.48

and

{log}_{10} r = - 0.45

, then the sum of mantissas of

p, q

and

r

If $\frac{{(p + \frac{1}{q})}^{p - q} {(p - \frac{1}{q})}^{p + q}}{{(q + \frac{1}{p})}^{p - q} {(q - \frac{1}{p})}^{p + q}} = {(\frac{p}{q})}^{x}, then x =_________.$

Q. If the ratio of the roots of

l x^{2} + n x + n = 0

is p:q, then

Q. If

P

is the number of natural numbers whose logarithm to the base

10

have the characteristic

p

and

Q

is the number of natural numbers logarithm of whose reciprocals to the base

10

have the characteristic

- q

, then find the value of

{log}_{10} P - {log}_{10} Q

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log10p+log10q=log10(p−q) then

The correct option is B p=q1−qlog10p+log10q=log10(p−q)log10pq=log10(p−q)pq=p−qp(q−1)=−qp=q1−q

${log}_{10} p + {log}_{10} q = {log}_{10} (p - q)$ then

The correct option is B $p = \frac{q}{1 - q}$
${log}_{10} p + {log}_{10} q = {log}_{10} (p - q)$
${log}_{10} p q = {log}_{10} (p - q)$
$p q = p - q$
$p (q - 1) = - q$
$p = \frac{q}{1 - q}$