Question

the value of 1/3 log 125 base 10 - 2 log 4 base 10 + log 32 base 10=​

Answer 1

log(125)¹/³+log32-log16

log5*32/16

log10

1

Answer 2

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

Step-by-step explanation:

Given : Expression $\frac{1}{3}\log_{10} 125-2\log_{10} 4+\log_{10}32$

To find : The value of the expression ?

Solution :

Applying logarithmic property, $a\log x=\log x^a$

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

$=\log_{10} (5^3)^{\frac{1}{3}}-\log_{10} 16+\log_{10}32$

$=\log_{10} 5-\log_{10} 16+\log_{10}32$

Using property, $\log ab=\log a+\log b$ and $\log (\frac{a}{b})=\log a-\log b$

$=\log_{10} \frac{5\times 32}{16}$

$=\log_{10} 10$

$=1$

Therefore, $\frac{1}{3}\log_{10} 125-2\log_{10} 4+\log_{10}32=1$

#Learn more

If log 16+2 log 2 /log 4=x then find the value of x​

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