Let for real .

MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

Let

g(x)=5\cdot 10^{2x-1}

for real

x

. (i) Rewrite

g(x)

in the form

k\,a^{x}

, where

k

and

a

are positive constants independent of

x

. (ii) Find

g'(x)

. (iii) Evaluate

g'(\log_{10}5)

. (Here

\log_{10}

denotes the logarithm to base

10

.)

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