Problem

For \(E(x)~=~5\cdot~2^{x}\) with points \((0,~5)\), \((1,~10)\), and \((2,~20)\), determine its logarithmic inverse. State the inverse equation, reversed points, domain, range, vertical asymptote, and behavior.

Actual exponential source graph without its inverse curve.

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inverse equation = L(x)=5log₂(x); reversed points = (5,0),(10,1),(20,2); domain = (0,∞); range = (-∞,∞); vertical asymptote = x=0; behavior = increasing

inverse equation = L(x)=log₂(x)/5; reversed points = (5,0),(10,1),(20,2); domain = (0,∞); range = (-∞,∞); vertical asymptote = x=0; behavior = increasing

inverse equation = L(x)=log₂(x-5); reversed points = (5,0),(10,1),(20,2); domain = (5,∞); range = (-∞,∞); vertical asymptote = x=5; behavior = increasing

inverse equation = L(x)=log₂(x/5); reversed points = (5,0),(10,1),(20,2); domain = (0,∞); range = (-∞,∞); vertical asymptote = x=0; behavior = increasing

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For \(E(x)~=~5\cdot~2^{x}\) with points \((0,~5)\), \((1,~10)\), and \((2,~20)\), determine its logarithmic inverse. State the inverse equation, reversed points, domain, range, vertical asymptote, and behavior.

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