Question

Find n if
$(1\frac{1}{3} {)}^{n} - (1 \times \frac{1}{3}) = \frac{28}{27}$
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Answer 1

Step-by-step explanation:

$(1 \frac{ 1 }{ 3 } ) ^ { x } -(1 \times \frac{ 1 }{ 3 } )= \frac{ 28 }{ 27 }$

$\left(\frac{3+1}{3}\right)^{x}-1\times \left(\frac{1}{3}\right)=\frac{28}{27}$

$\left(\frac{4}{3}\right)^{x}-1\times \left(\frac{1}{3}\right)=\frac{28}{27}$

$\left(\frac{4}{3}\right)^{x}-\frac{1}{3}=\frac{28}{27}$

$\left(\frac{4}{3}\right)^{x}-\frac{1}{3}-\frac{28}{27}=0$

$\left(\frac{4}{3}\right)^{x}-\frac{37}{27}=0$

$\left(\frac{4}{3}\right)^{x}=\frac{37}{27}$

$\log(\left(\frac{4}{3}\right)^{x})=\log(\frac{37}{27})$

$x\log(\frac{4}{3})=\log(\frac{37}{27})$

$x=\frac{\log(\frac{37}{27})}{\log(\frac{4}{3})}$

$x=\log_{\frac{4}{3}}\left(\frac{37}{27}\right)$