Given log5 y = n. Express 53n + 2 in terms of y.

log5 y = n5n = yConsider 5n = y⇒ `(5^n)^3=y^3`⇒ `5^(3n)=y^3` ⇒ `5^(3n) xx 5^2 = y^3 xx 5^2`⇒` 5^(3n+2) = 25y^3`

Given Log5 Y = N. Express 53n + 2 In Term of Y. - Mathematics

Given log₅y = n. Express 5^{3n + 2} in terms of y.

Sum

log₅y = n
5ⁿ = y
Consider 5ⁿ = y
⇒ `(5^n)^3=y^3`
⇒ `5^(3n)=y^3`
⇒ `5^(3n) xx 5^2 = y^3 xx 5^2`
⇒` 5^(3n+2) = 25y^3`

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Interchanging Logarithmic and Exponential Forms

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Chapter 8: Logarithms - Exercise 8 (A) [Page 104]

Chapter 8 Logarithms
Exercise 8 (A) | Q 9.2 | Page 104