Exponential and Logarithmic Summary

Algebra 2 · Axiom Academy

SUMMARY Exponential and Logarithmic Functions Let's review how exponential and logarithmic functions model growth, decay, and their reversal throughout science and finance. Exponential and logarithmic functions are inverses of each other: means exactly the same thing as b^y=x , and their graphs reflect across the line y=x . The three logarithm properties — product, quotient, and power — convert multiplication, division, and exponents inside a log into addition, subtraction, and multiplication outside it, which is what makes log equations solvable. The natural base arises from continuous compounding, , and underlies every continuous-growth model in finance and the sciences. Solving strategy depends on the equation: same-base exponential equations reduce to setting exponents equal; different-base equations require taking a logarithm of both sides; logarithmic equations require condensing to a single log, then exponentiating — and always checking for extraneous solutions. These functions aren't just algebra — they describe real, measurable change across science and finance, anywhere a quantity grows or decays at a rate proportional to its own size. Core Concept Exponential Functions & the Number e The general exponential function f(x)=ab^x requires and . When the function grows without bound; when it decays toward zero. Every exponential function has a horizontal asymptote that the graph approaches but never touches.

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