How do you write $64=4^x$ in Logarithm form?

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Answer 1 · 2016-09-01T12:54:14

$log_4 64 = x$

(this follows from the basic definition of log)

Answer 2 · 2016-09-01T13:04:55

$log_color(red)(a) color(blue)(b) = color(lime)(c) hArr color(red)(a)^color(lime)(c) = color(blue)(b)$

$log_color(red)(4) color(blue)(64) = color(lime)(x) hArr color(red)(4)^color(lime)(x) = color(blue)(64)$

"The $color(red)("base")$ stays the $color(red)("base")$ , and the other two change around"

log form and index form are interchangeable:

By definition: $log_color(red)(a) color(blue)(b) = color(lime)(c) hArr color(red)(a)^color(lime)(c) = color(blue)(b)$

Remember the following:

"The $color(red)("base")$ stays the $color(red)("base")$ , and the other two change around"

$log_color(red)(4) color(blue)(64) = color(lime)(x) hArr color(red)(4)^color(lime)(x) = color(blue)(64)$

$log_color(red)(4) color(blue)(64) = color(lime)(3) hArr color(red)(4)^color(lime)(3) = color(blue)(64)$

How do you write 64=4^x64=4^x in Logarithm form?