How do you solve for x in $6.428 = {1.263}^{x}$ $6.428 = 1.263 ^ (x)$ ?

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Answer 1 · 2016-04-28T23:14:07

I found: $x = 7.9689$ $x=7.9689$

Take the natural log of both sides:

$ln 6.428 = ln {1.263}^{x}$ $color(red)(ln)6.428=color(red)(ln)1.263^x$

use the property of logs on the exponent of the argument:

$ln 6.428 = x ln 1.263$ $color(red)(ln)6.428=color(blue)(x)color(red)(ln)1.263$

rearrange:

$x = \frac{ln (6.428)}{ln (1.263)} = 7.9689$ $x=(ln(6.428))/(ln(1.263))=7.9689$

How do you solve for x in 6.428=1.263x6.428 = 1.263 ^ (x)?