MHB Using Log Laws and values to compute this compution

[cbarker1]

Using logs to compute the following, to the four-figure accuracy. $\frac{.009292}{(\sqrt[3]{582400}+14.23)}$

Let N=$\frac{.009292}{(\sqrt[3]{582400}+14.23)}$, then
$\log\left({N}\right)=\log\left({\frac{.009292}{(\sqrt[3]{582400}+14.23)}
}\right)$.

Log N=

$\log\left({.09292}\right)-\log\left({\sqrt[3]{582400}+14.23}\right)$

What to do with the logarithm after the subtraction sign?the answer in the back of the book is 9.507*10^(-4)

 

[I like Serena]

Using logs to compute the following, to the four-figure accuracy. $\frac{.009292}{(\sqrt[3]{582400}+14.23)}$

Let N=$\frac{.009292}{(\sqrt[3]{582400}+14.23)}$, then
$\log\left({N}\right)=\log\left({\frac{.009292}{(\sqrt[3]{582400}+14.23)}
}\right)$.

Log N=

$\log\left({.09292}\right)-\log\left({\sqrt[3]{582400}+14.23}\right)$

What to do with the logarithm after the subtraction sign?

You might substitute:
$$\sqrt[3]{582400} = 10^{\log(\sqrt[3]{582400})} = 10^{\frac 1 3 \log 582400}$$