Penjelasan dengan langkah-langkah:
[tex]1. \: {13}^{ {x}^{2} - 5x - 14 } = 1 \\ {13}^{ {x}^{2} - 5x - 14} = {13}^{0} \\ {x}^{2} - 5x - 14 = 0 \\ (x - 7)(x + 2) = 0 \\ x = 7 \: atau \: x = - 2 [/tex]
[tex]2. \: {( \frac{1}{4}) }^{x + 2} = \sqrt[4]{16} \\ { (\frac{1}{ {2}^{2} }) }^{x + 2} = \sqrt[4]{ {2}^{4} } \\ { ({2}^{ - 2}) }^{x + 2} = {2}^{1} \\ {2}^{ - 2x - 4} = {2}^{1} \\ - 2x - 4 = 1 \\ - 2x = 5 \\ x = - \frac{5}{2} [/tex]
[tex]3. \: {2}^{3x - 8} = 16 \\ {2}^{3x - 8} = {2}^{4} \\ 3x - 8 = 4 \\ 3x = 12 \\ x = 4[/tex]
[tex] {36}^{x + 5} = { (\frac{1}{216}) }^{x - 1} \\ {( {6}^{2}) }^{x + 5} = {( \frac{1}{ {6}^{3} }) }^{x - 1} \\ {6}^{2x + 10} = { ({6}^{ - 3}) }^{x - 1} \\ {6}^{2x + 10} = {6}^{ - 3x + 3} \\ 2x + 10 = - 3x + 3 \\ 2x + 3x = 3 - 10 \\ 5x = - 7 \\ x = - \frac{7}{5} [/tex]
[tex]5. \: {6}^{2 {x}^{2} + 8x - 10} = {3}^{2 {x}^{2} + 8x - 10} \\ {(2 \times 3)}^{2 {x}^{2} + 8x - 10} = {3}^{2 {x}^{2} + 8x - 10 } \\ {2}^{2 {x}^{2} + 8x - 10} \times {3}^{2 {x}^{2} + 8x - 10} = {3}^{2 {x}^{2} + 8x - 10 } \\ {2}^{2 {x}^{2} + 8x - 10 } = \frac{ {3}^{2 {x}^{2} + 8x - 10 } }{ {3}^{2 {x}^{2} + 8x - 10} } \\ {2}^{2 {x}^{2} + 8x - 10 } = 1 \\ {2}^{2 {x}^{2} + 8x - 10 } = {2}^{0} \\ 2 {x}^{2} + 8x - 10 = 0 \\ (2x + 10)(x - 1) = 0 \\ 2x = - 10 \: atau \: x = 1 \\ x = - 5 \: atau \: x = 1 [/tex]
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