# How do you change  2^0.4 = 1.320 into log form?

Sep 10, 2016

${2}^{0.4} = 1.320 \Leftrightarrow {\log}_{2} 1.320 = 0.4$

#### Explanation:

log form and index form give the same information and are interchangeable.

${\log}_{a} b = c \Leftrightarrow {a}^{c} = b$

"The base stays the base and the other two swop around"

${2}^{0.4} = 1.320 \Leftrightarrow {\log}_{2} 1.320 = 0.4$

In index form: ${2}^{1} = 2 , \text{ so } {2}^{0.4}$ will be less than 2.
The value 1.320 seems reasonable.

In log form, the question is, "What power or index of 2 will give 0.4?"