Question

log of x to the base √27 = 8/3
solve​

Answer 1

Answer:

x = 81

Step-by-step explanation:

$Given: log_{\sqrt{27}} (x) = \frac{8}{3}$

$\Rightarrow log_{\sqrt{27}} (x) = log_{\sqrt{27}} ((\sqrt{27})^{\frac{8}{3})}$

$\Rightarrow log_{\sqrt{27}} (x) = log_{\sqrt{27}} [({27})^{\frac{1}{2}*\frac{8}{3}}]$

$\Rightarrow log_{\sqrt{27}} (x) = log_{\sqrt{27}} [({27})^{\frac{4}{3}]$

$\Rightarrow log_{\sqrt{27}} (x) = log_{\sqrt{27}} [({3^3})^{*\frac{4}{3}}]$

$\Rightarrow log_{\sqrt{27}} (x) = log_{\sqrt{27}} [3^4}]$

$\Rightarrow log_{\sqrt{27}} (x) = log_{\sqrt{27}} [81}]$

$\Rightarrow \textbf x = 81$

Hope it helps!

Answer 2

Answer:

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