When and why do you log-transform a variable?

easy

Answer

$(1) Right-skewed positive variables (income, prices, response times): log transform pulls in the tail, makes distribution more symmetric, often more Gaussian.$
$(2) Multiplicative relationships become additive after log — foundation of Box-Cox / Yeo-Johnson and log-linear models.$
$(3) Improves linearity for regression.$
$\operatorname{log}(0)$
$Not helpful for symmetric or already-Gaussian data.$

Check yourself — multiple choice

Always log
Right-skewed positive vars: log makes symmetric / more Gaussian, converts multiplicative to additive; handle zeros with $\operatorname{log}(1 + x)$
Only for negative data
Never useful

Log transform: right-skewed positive vars → symmetry + linearity; handle zeros.

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