Question

The value of [13log10(125) - 2log10(4) + log10(32)] :

A) 0 B) 1 C) 2 D) 4/5

Answer 1

Step-by-step explanation:

The value of [1/3log10(125) - 2log10(4) + log10(32)]

=log10[125]⅓-log10[4]²+log10[32]

=log10[5] + log10[32/16]

,=log10[5×2]

=1

so opt b

Answer 2

The required solution is $\frac{1}{3}log_{10}^{125} -2log_{10}^{4} +log_{10}^{32}=1$.

Given:

$\frac{1}{3} log_{10}^{125} -2log_{10}^{4} +log_{10}^{32}$

To find:

the simplified form of the given expression.

Solution:

We can find the solution to this problem in the following way.

We can write the logarithm of a number assigning the natural base e or any other base. Here the base of the logarithm is 10 throughout the expression.

We know the application of logarithm to any number which can be written as the square or any index, reduces the number as under.

$log_{base}^{number^{index}=(index)log_{base}^{number}$

(We shall use all the relevant formulae in the solution to this problem.)

We can simplify the expression as follows.

$\frac{1}{3}log_{10}^{125} -2log_{10}^{4} +log_{10}^{32}\\=\frac{1}{3}log_{10}^{5^{3} } -2log_{10}^{2^{2} } +log_{10}^{2^{5} }\\=\frac{1}{3}\times 3log_{10}^{5} -4log_{10}^{2} +5log_{10}^{2}\\=log_{10}^{5} +log_{10}^{2}\\=log_{10}^{5\times 2}\\=log_{10}^{10}\\=1$

The required solution is the simplified form of the expression $\frac{1}{3}log_{10}^{125} -2log_{10}^{4} +log_{10}^{32}=1$.

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