If log 2 y = x and log 3 z = x, find 72 x in terms of y and z.

Given, log 2 y = x and log 3 z = x ⇒ y = 2 x and z = 3 x . (72) x = (2 3 .3 2 ) x = (2) 3x .(3) 2x = (2 x ) 3 .(3 x ) 2 = (y) 3 .(z) 2 Hence, (72) x = y 3 .z 2 .

|

Mathematics

If log₂y = x and log₃z = x, find 72^x in terms of y and z.

Logarithms

65 Likes

Answer

Given,

log₂y = x and log₃z = x

⇒ y = 2^x and z = 3^x.

(72)^x = (2³.3²)^x

= (2)^3x.(3)^2x

= (2^x)³.(3^x)²

= (y)³.(z)²

Hence, (72)^x = y³.z².

Answered By

39 Likes

Mathematics

If log₂y = x and log₃z = x, find 72^x in terms of y and z.

Logarithms

Answer

Related Questions

Given log₁₀a = m and log₁₀b = n, express $\dfrac{a^3}{b^2}$ in terms of m and n.

Given log₁₀x = 2a and log₁₀y = $\dfrac{b}{2}$ ,
(i) write 10^a in terms of x.
(ii) write 10^{2b + 1} in terms of y.
(iii) if log₁₀P = 3a - 3b, express P in terms of x and y.

If log₂x = a and log₅y = a, write 100^{2a - 1} in terms of x and y.

Simplify the following :
log a³ - log a²

Mathematics

If log2y = x and log3z = x, find 72x in terms of y and z.

Logarithms

Answer

Related Questions

Given log10a = m and log10b = n, express a3b2\dfrac{a^3}{b^2}b2a3​ in terms of m and n.

Given log10x = 2a and log10y = b2\dfrac{b}{2}2b​,(i) write 10a in terms of x.(ii) write 102b + 1 in terms of y.(iii) if log10P = 3a - 3b, express P in terms of x and y.

If log2x = a and log5y = a, write 1002a - 1 in terms of x and y.

Simplify the following :log a3 - log a2

If log₂y = x and log₃z = x, find 72^x in terms of y and z.

Given log₁₀a = m and log₁₀b = n, express $\dfrac{a^3}{b^2}$ in terms of m and n.

Given log₁₀x = 2a and log₁₀y = $\dfrac{b}{2}$ ,
(i) write 10^a in terms of x.
(ii) write 10^{2b + 1} in terms of y.
(iii) if log₁₀P = 3a - 3b, express P in terms of x and y.

If log₂x = a and log₅y = a, write 100^{2a - 1} in terms of x and y.

Simplify the following :
log a³ - log a²