Section 6.3 : Solving Exponential Equations
Solve each of the following equations.
- \({11^{4 + x}} = {11^{7 - 10x}}\)
- \({3^{4x}} = {3^{7x}}\)
- \({2^{1 - x}} = {2^{2 - 3x}}\)
- \({9^{{x^{\,2}}}} = {9^{12 - 4x}}\)
- \({6^{{x^{\,2}} - 3x}} = {6^{20 + 5x}}\)
- \(\displaystyle {6^{1 + x}} = \frac{1}{{{{36}^{4x + 2}}}}\)
- \({9^x} = {27^{2 + x}}\)
- \({8^{4x + 1}} = 1\)
- \(3 = {14^{9 - 2x}}\)
- \({6^{2 + x}} = {8^{8 + 2x}}\)
- \({13^{5 + 7x}} = {2^{3 - x}}\)
- \({10^{7x}} = 3\)
- \(16 = {10^{2 + 3x}}\)
- \(6 = {{\bf{e}}^{4 + 9x}}\)
- \(9 - {{\bf{e}}^{6x}} = 0\)
- \({{\bf{e}}^{{x^{\,2}} - 2}} = 4\)