Question - Solving an Exponential Equation
Solution:
The equation in the image is:$$2^{3x+5} = 2^{1-x}$$To solve for $$x$$, since the bases are the same, you can set the exponents equal to each other:$$3x + 5 = 1 - x$$Now, solve for $$x$$:Add $$x$$ to both sides:$$3x + x + 5 = 1 - x + x$$$$4x + 5 = 1$$Subtract 5 from both sides:$$4x + 5 - 5 = 1 - 5$$$$4x = -4$$Divide both sides by 4:$$x = -4 / 4$$$$x = -1$$
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