Question

find the value of x if 3^5x * 81² * 6561/3^2x = 3⁷​

Answer 1

Dear student

$$\begin{gathered} 3^{5\mathrm{x}}\times {81}^2\times \frac{6561}{3^{2\mathrm{x}}}=3^7 \\ {3}^{5\mathrm{x}}\times {\left(3^4\right)}^2\times \frac{3^8}{3^{2\mathrm{x}}}=3^7 \\ {3}^{5\mathrm{x}}\times 3^8\times 3^{8-2\mathrm{x}}=3^7\left[{\left({\mathrm{a}}^{\mathrm{m}}\right)}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{mn}}\mathrm{and}\frac{{\mathrm{a}}^{\mathrm{m}}}{{\mathrm{a}}^{\mathrm{n}}}={\mathrm{a}}^{\mathrm{m}-\mathrm{n}}\right] \\ {3}^{5\mathrm{x}+8+8-2\mathrm{x}}=3^7 \\ \mathrm{When}\mathrm{bases}\mathrm{are}\mathrm{same}\mathrm{we}\mathrm{can}\mathrm{equate}\mathrm{powers}. \\ 3\mathrm{x}+16=7 \\ 9=-3\mathrm{x} \\ \boxed{\mathrm{x}=-3} \end{gathered}$$
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