Given that t = $2 ^{-x}$, find $2 ^{x + 1}$ in terms of t.

Assessment: WAEC SSCE - General Mathematics - 2017 (Objective) Subject: General Mathematics

Question 1 Report

$\frac{2}{t}$

$\frac{t}{2}$

$\frac{1}{2t}$

t

Answer Details

We can start by using the laws of exponents to rewrite $2^{x+1}$ in terms of $2^{-x}$, which is given by $t$. Recall that $a^{m+n} = a^m \times a^n$ and $a^{-n} = \frac{1}{a^n}$. Therefore, we have: $$2^{x+1} = 2^x \times 2^1 = 2^x \times 2 = 2 \times 2^x$$ Next, we can substitute $2^{-x} = t$ into this expression: $$2 \times 2^x = 2 \times \frac{1}{t} = \frac{2}{t}$$ So the answer is: $\frac{2}{t}$.

Read lesson note on Logarithms (WAEC)

Logarithms

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