CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Mass Energy Equivalence

If a2=b3=c5...

Question

If $a^{2} = b^{3} = c^{5} = d^{6}$ then show that ${log}_{d}^{a b c} = \frac{31}{5}$

Open in App

Solution

$\begin{matrix} A t f i r s t a^{2} = d^{6} \Rightarrow a = {(d^{6})}^{\frac{1}{2}} b^{3} = d^{6} \Rightarrow a = {(d^{6})}^{\frac{1}{3}} c^{5} = d^{6} \Rightarrow a = {(d^{6})}^{\frac{1}{5}} N o w, s u b s t i t u t e t h e v a l u e o f a, b, a n d c i n t e r m d i n t h e l o g a r i t h m i c t e r m . l o g_{d} a b c = {log}_{d} ⎡ ⎢ ⎣ {(d^{6})}^{\frac{1}{2}} {(d^{6})}^{\frac{1}{3}} {(d^{6})}^{\frac{1}{5}} ⎤ ⎥ ⎦ = {log}_{d} {(d^{6})}^{\frac{1}{2} + \frac{1}{3} + \frac{1}{5}} (b y u sin g p r o d u c t r u l e o f o n e n t s) = {log}_{d} {(d^{6})}^{\frac{15 + 10 + 6}{30}} = {log}_{d} {(d^{6})}^{\frac{31}{30}} = {log}_{d} {(d)}^{6 \times \frac{31}{30}} = {log}_{d} {(d)}^{\frac{31}{5}} B y u sin g p o w e r r u l e o f log a r i t h m s = \frac{31}{5} \times {log}_{d} d = \frac{31}{5} \times 1 [B y u sin g log a r i t h m o f b a s e r u l e] = \frac{31}{5} H e n c e, l o g_{d} a b c = \frac{31}{5} p r o v e d . \end{matrix}$

Suggest Corrections

thumbs-up

0

Similar questions

a^{2} = b^{3} = c^{5} = d^{6}

{log}_{d} a b c = \frac{31}{5}

If a + b + c = 0

Then prove that

a⁵+ b⁵+ c⁵ a³ + b³+ c³a²+ b²+ c²

------------------- = ---------------------- × --------------------------

5 3 2

a + b + c = 0

6 (a^{5} + b^{5} + c^{5}) = 5 (a^{3} + b^{3} + c^{3}) (a^{2} + b^{2} + c^{2})

a + b + c + d = 0

\frac{a^{5} + b^{5} + c^{5} + d^{5}}{4} = \frac{a^{3} + b^{3} + c^{3} + d^{3}}{3} \cdot \frac{a^{2} + b^{2} + c^{2} + d^{2}}{2}

a + b + c = 10

a, b, c > 0

. Then the maximum value of

a^{2} b^{3} c^{5}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Mass - Energy Equivalence

PHYSICS

Watch in App

explore_more_icon

Explore more

Mass Energy Equivalence

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon