Logarithm Base Change + Exponent Checks — Notebook Template

Compute logs in different bases, convert between ln/log10/log_b, and verify with exponentiation.

math logarithms algebra

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What this template does

This is a ready-to-run GetCalcMaster Notebook starter. Open it into Notebook, run once with defaults, then tweak inputs and keep your assumptions next to the math.

How to use it (recommended)

Open in Notebook.
Set x and base b (b>0, b≠1).
Compute log_b(x) using ln(x)/ln(b).
Verify by raising b^(log_b(x)) ≈ x.
Snapshot the final values and assumptions.

Tip: When a result matters, verify it twice: a unit check + a second method (graph/estimate).

Preview (first cells)

This preview is for readability. The full template loads into Notebook when you click Open.

TEXT

# Logarithm Base Change

Base-change formula:

**log_b(x) = ln(x) / ln(b)**

(Works for any valid base b.)

MATH

x = 500

MATH

b = 2

MATH

log_b = ln(x) / ln(b)

MATH

log_b

MATH

# Verification: b^(log_b(x)) ≈ x
x_check = b^(log_b)