How do you change $2^{0.4} = 1.320$ $2^0.4 = 1.320$ into log form?

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Answer 1 · 2016-09-10T07:02:54

$2^{0.4} = 1.320 \Leftrightarrow {log}_{2} 1.320 = 0.4$ $2^0.4 = 1.320 hArr log_2 1.320 = 0.4$

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

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

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

$2^{0.4} = 1.320 \Leftrightarrow {log}_{2} 1.320 = 0.4$ $2^0.4 = 1.320 hArr log_2 1.320 = 0.4$

In index form: $2^{1} = 2, so 2^{0.4}$ $2^1 = 2, " so " 2^0.4$ 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?"

How do you change 20.4=1.320 2^0.4 = 1.320 into log form?