What is the common logarithm of 54.29?

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What is the common logarithm of 54.29?

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Answer 1 · 2015-09-10T11:44:00

$log (54.29) \approx 1.73472$ $log(54.29) ~~ 1.73472$

Explanation:

$x = log (54.29)$ $x = log(54.29)$ is the solution of $10^{x} = 54.29$ $10^x = 54.29$

If you have a natural log ( $ln$ $ln$ ) function but not a common $log$ $log$ function on your calculator, you can find $log (54.29)$ $log(54.29)$ using the change of base formula:

${log}_{a} (b) = \frac{{log}_{c} (b)}{{log}_{c} (a)}$ $log_a(b) = log_c(b)/log_c(a)$

So:

$log (54.29) = {log}_{10} (54.29) = \frac{{log}_{e} (54.29)}{{log}_{e} (10)} = \frac{ln (54.29)}{ln (10)}$ $log(54.29) = log_10(54.29) = log_e(54.29)/log_e(10) = ln(54.29)/ln(10)$

Answer 2 · 2015-09-10T20:31:13

If you are using tables, you need:

Explanation:

$log 54.29 = log (5.429 \times 10^{1})$ $log54.29 = log(5.429 xx 10^1)$

log(5.429) +1.

From tables

$log 5.42 = 0.73400$ $log5.42 = 0.73400$

$log 5.43 = 0.73480$ $log5.43 = 0.73480$

$5.429$ $5.429$ is $\frac{9}{10}$ $9/10$ of the way from $5.42 to 5.43$ $5.42 " to " 5.43$ , so we get
$\frac{9}{10} = \frac{x}{80}$ $9/10 = x/80$ so $x = 72$ $x=72$

by linear interpolation,

$log (5.429) = 0.74372$ $log(5.429) = 0.74372$

So
$log (54.29) = 1.74372$ $log(54.29) = 1.74372$

(I'm using $=$ $=$ rather than $\approx$ $~~$ in each case.)

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What is the common logarithm of 54.29?

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