If log 10 a = b, find 10 3b - 2 in terms of a.

Given, ⇒ log 10 a = b ⇒ 10 b = a Cubing both sides, we get : ⇒ (10 b ) 3 = a 3 ⇒ 10 3b = a 3 Dividing both sides by 10 2 , we get : Hence, 10 3b - 2 =

Mathematics

If log₁₀ a = b, find 10^{3b - 2} in terms of a.

Logarithms

30 Likes

Answer

Given,

⇒ log₁₀ a = b

⇒ 10^b = a

Cubing both sides, we get :

⇒ (10^b)³ = a³

⇒ 10^3b = a³

Dividing both sides by 10², we get :

$\Rightarrow \dfrac{10^{3b}}{10^2} = \dfrac{a^3}{10^2} \\[1em] \Rightarrow 10^{3b - 2} = \dfrac{a^3}{100}.$

Hence, 10^{3b - 2} = $\dfrac{a^3}{100}.$

Answered By

16 Likes

Mathematics

If log₁₀ a = b, find 10^{3b - 2} in terms of a.

Logarithms

Answer

Related Questions

If log₁₀ 8 = 0.90; find the value of :
(i) log₁₀ 4
(ii) log $\sqrt{32}$
(iii) log 0.125

If log 27 = 1.431, find the value of :
(i) log 9
(ii) log 300

If log₅ x = y, find 5^{2y + 3} in terms of x.

Given :
log₃ m = x and log₃ n = y
(i) Express 3^{2x - 3} in terms of m.
(ii) Write down 3^{1 - 2y + 3x} in terms of m and n.
(iii) If 2 log₃ A = 5x - 3y; find A in terms of m and n.

Mathematics

If log10 a = b, find 103b - 2 in terms of a.

Logarithms

Answer

Related Questions

If log10 8 = 0.90; find the value of :(i) log10 4(ii) log 32\sqrt{32}32​(iii) log 0.125

If log 27 = 1.431, find the value of :(i) log 9(ii) log 300

If log5 x = y, find 52y + 3 in terms of x.

Given :log3 m = x and log3 n = y(i) Express 32x - 3 in terms of m.(ii) Write down 31 - 2y + 3x in terms of m and n.(iii) If 2 log3 A = 5x - 3y; find A in terms of m and n.

If log₁₀ a = b, find 10^{3b - 2} in terms of a.

If log₁₀ 8 = 0.90; find the value of :
(i) log₁₀ 4
(ii) log $\sqrt{32}$
(iii) log 0.125

If log 27 = 1.431, find the value of :
(i) log 9
(ii) log 300

If log₅ x = y, find 5^{2y + 3} in terms of x.

Given :
log₃ m = x and log₃ n = y
(i) Express 3^{2x - 3} in terms of m.
(ii) Write down 3^{1 - 2y + 3x} in terms of m and n.
(iii) If 2 log₃ A = 5x - 3y; find A in terms of m and n.