Question

How do you solve log base 3 (27) by hand

Answer 1

$\bf \textit{Logarithm Cancellation Rules}\\\\ \boxed{log_a a^x= x}\qquad \qquad a^{log_ax}=x\\\\ -------------------------------\\\\ log_3(27)\qquad \boxed{27=3^3}\qquad log_3(3^{\underline{3}})\implies \underline{3}$

Answer 2

Rewrite as an equation.log3(27)=xlog3(27)=xRewrite log3(27)=xlog3(27)=x in exponential form using the definition of a logarithm. If xx and bb are positive real numbers and bb does not equal 11, then logb(x)=ylogb(x)=y is equivalent to by=xby=x.3x=273x=27Create equivalent expressions in the equation that all have equal bases.3x=333x=33Since the bases are the same, the two expressions are only equal if the exponents are also equal.x=3x=3The variable x is equal to 33.3