Logarithms and Exponentials Formulas, Exams of Business Systems

A concise collection of formulas and graphical representations related to logarithms and exponentials, essential for a-level mathematics. It includes key identities, rules for manipulating logarithmic expressions, and graphical interpretations of exponential and logarithmic functions. The resource is designed to aid students in understanding and applying these concepts in problem-solving and exam preparation, offering a quick reference for important mathematical relationships and visual aids for better comprehension. It also covers transformations and properties of logarithmic and exponential functions, enhancing students' analytical skills.

Typology: Exams

2025/2026

Available from 09/14/2025

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Edexcel A Level Math - Logarithms and
Exponentials formulas
f(x)v=veˣ,vf'(x)v=
f(x)v=veᵏˣ,vf'(x)v=v-v
vkeᵏˣ
Makevxvthevsubjectvofvv=vnv-vxv=vlogₐ(n)
logₐ(x)v+vlogₐ(y)
logₐ(x)v-vlogₐ(y)
logₐ(xᵏ)v-vlogₐ(xy)
logₐ(x/y)
klogₐ(x)
logₐ(1/x)
logₐ(a)
logₐ(1)v-v-logₐ(x)
1
0
pf2

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Edexcel A Level Math - Logarithms and

Exponentials formulas

f(x)v=veˣ,vf'(x)v= f(x)v=veᵏˣ,vf'(x)v=v-veˣ vkeᵏˣ Makevxvthevsubjectvofvaˣv=vnv-vxv=vlogₐ(n) logₐ(x)v+vlogₐ(y) logₐ(x)v-vlogₐ(y) logₐ(xᵏ)v-vlogₐ(xy) logₐ(x/y) klogₐ(x) logₐ(1/x) logₐ(a) logₐ(1)v-v-logₐ(x) 1 0

Statevthevnumbervthatvthevbasevofvavlogvcannotvbe Statevavreasonvwhyvavsolutionvtovavquadraticvmayvbevnotvbevthevsolutionvtovthevlogv-vBasevcannotvequalv 1 Thevvaluevinsidevofvthevlogvcannotvnegative Drawvanvexponentialvandvlogarithmvgraphv- vhttps://people.richland.edu/james/lecture/m116/logs/log2.gif ln(x)v=v log(x)v=v-vlogₑ(x) log₁₀(x) Whenvyv=vaxⁿ,vstatevthevgraphvthatvwillvproducevavstraightvlinev- vlog(y)vagainstvlog(x)vwithvgradientvnvandvverticalvinterceptvlog(a) Whenvyv=vabˣ,vstatevthevgraphvthatvwillvproductvavstraightvlinev- vlog(y)vagainstvxvwithvgradientvlog(b)vandvverticalvinterceptvlog(a)