Question

Solve the following exponential equation ="TexFormula1" title="3 {}^{2x } - 9 = 0" alt="3 {}^{2x } - 9 = 0" align="absmiddle" class="latex-formula">
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Answer 1

Answer:

x = 1

Step-by-step explanation:

Given exponential equation:

$3^{2x}-9=0$

Add 9 to both sides of the equation:

$\implies 3^{2x}-9+9=0+9$

$\implies 3^{2x}=9$

$\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:$

$\implies \left(3^2\right)^{x}=9$

$\implies9^{x}=9$

$\textsf{Apply exponent rule} \quad a=a^1:$

$\implies9^{x}=9^1$

$\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):$

$\implies x=1$

Answer 2

3*2x-3*2=0
2x-2=0
2x=2|:2
x=1