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Formula
Solve the equation
Answer
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Graph
$y = 25 ^ { 2 x - 1 }$
$y = 5 ^ { x + 4 }$
$y$Intercept
$\left ( 0 , \dfrac { 1 } { 25 } \right )$
Asymptote
$y = 0$
$y$Intercept
$\left ( 0 , 625 \right )$
Asymptote
$y = 0$
$25 ^{ 2x-1 } = 5 ^{ x+4 }$
$x = 2$
Solve the equation
$\color{#FF6800}{ 25 } ^ { \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } = \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } }$
$ $ Solve the exponential equation (inequality) by unifying the bases of the exponents $ $
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) = \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) = x + 4$
$ $ Multiply each term in parentheses by $ 2$
$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } = x + 4$
$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ x } - 2 = x + 4$
$ $ Simplify the expression $ $
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } - 2 = x + 4$
$4 x - 2 = \color{#FF6800}{ x } + 4$
$ $ Move the variable to the left-hand side and change the symbol $ $
$4 x - 2 \color{#FF6800}{ - } \color{#FF6800}{ x } = 4$
$4 x \color{#FF6800}{ - } \color{#FF6800}{ 2 } - x = 4$
$ $ Move the constant to the right side and change the sign $ $
$4 x - x = 4 \color{#FF6800}{ + } \color{#FF6800}{ 2 }$
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ x } = 4 + 2$
$ $ Organize the expression $ $
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } = 4 + 2$
$3 x = \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 2 }$
$ $ Add $ 4 $ and $ 2$
$3 x = \color{#FF6800}{ 6 }$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } = \color{#FF6800}{ 6 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 2 }$
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