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Chatty reference · maths1 week 6

85 words
1 min read
2026-08-16

6. Maths Week 6 — Logarithmic Functions

Official topics: logarithmic properties, graphs, exponential equations and logarithmic equations. citeturn1view0

Concepts

Definition:
log⁡bx=y  ⟺  by=x\log_b x=y\iff b^y=x
Properties:
log⁡b(xy)=log⁡bx+log⁡by\log_b(xy)=\log_bx+\log_by
log⁡b(xy)=log⁡bx−log⁡by\log_b\left(\frac{x}{y}\right)=\log_bx-\log_by
log⁡b(xk)=klog⁡bx\log_b(x^k)=k\log_bx
Change of base:
log⁡bx=log⁡axlog⁡ab\log_bx=\frac{\log_ax}{\log_ab}

Patterns

  1. Evaluate logs.
  2. Simplify logarithmic expressions.
  3. Convert log ↔ exponential form.
  4. Solve exponential equations.
  5. Solve logarithmic equations.
  6. Determine whether a solution is valid.
  7. Interpret logarithmic graphs.

Major trap

Whenever you manipulate logarithmic equations, domain restrictions matter.
You cannot blindly accept algebraic solutions.
Document outline

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