3^x=243 ⇒3^x=3× 3× 3× 3× 3 ⇒3^x=3^5 Since bases are same, we can equate the powers, ∴ x=5 ...

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Exponents with Unlike Bases and Same Exponent

Find x if ...

Question

Find $x$ if $3^{x} = 243$

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Solution

$3^{x} = 243$

$\Rightarrow 3^{x} = 3 \times 3 \times 3 \times 3 \times 3$

$\Rightarrow 3^{x} = 3^{5}$

Since bases are same, we can equate the powers,

$∴ x = 5$

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