Question

If log 8 = 0.9, then find а. Log 125​

Answer 1

The answer is short. We can solve it by properties of the logarithm.

$\log8=0.9\\\iff\log2^{3}=0.9\\\iff3\log2=0.9\\\iff\log2=0.3$

Hence,

$\large\red{\boxed{\red{\log2=0.3}}}$

Let's find our answer.

$\log125\\=\log5^{3}\\=\log\dfrac{10^{3}}{2^{3}}\\=\log10^{3}-\log2^{3}\\=3\log10-3\log2\\=3-(3\times0.3)\\=2.1\tiny{\text{\red{//}}}$

So,

$\large\red{\boxed{\red{\log125=\underline{2.1}}}}$

$\underline{2.1}$ is the correct answer.

$\large\underline{\text{Properties of the logarithm}}$

These are the properties of the logarithm under reals.

$\text{For }a>0,\ a\neq1\text{ and }x>0,\ y>0,$

(1)$\log_{a}a=1$, $\log_{a}1=0$

(2)$\log_{a}xy=\log_{a}x+\log_{a}y$

(3)$\log_{a}\dfrac{x}{y}=\log_{a}x-\log_{a}y$

(4)$\log_{a}x^{n}=n\log_{a}x$

Answer 2

$</p><p></p><p> </p><p></p><p></p><p>\tt{\implies}solution \: \: of \: question. \\ \\ </p><p></p><p> </p><p></p><p> </p><p>.</p><p></p><p>\tt{\implies} </p><p></p><p> </p><p>.</p><p></p><p>\tt{\implies}\begin{gathered}\log125\\ \\ =\log5^{3} \\ \\ </p><p></p><p> </p><p>.</p><p></p><p>\tt{\implies}</p><p></p><p> </p><p>.</p><p></p><p>\tt{\implies}=\log\dfrac{10^{3}}{2^{3}} \\ \\=\log10^{3}-\log2^{3}\\=3\log10-3\log2\\=3-(3\times0.3) \\ \\=2.1\tiny{\text{\red{//}}}\end{gathered}log125=log53=</p><p></p><p>So, \\ </p><p></p><p> </p><p></p><p> </p><p></p><p>\tt{\implies}\large\red{\boxed{\pink{\log125=\underline{2.1}}}} \\ log125=2.1</p><p></p><p>$