Question

Log10+2log3-log2 in single logarithm

Answer 1

log10+2log3-log2
=log10 + log3^2-log2
=log10+log9 - log2
=log (10x9)/2
=log 45



Here's ur answer

Answer 2

$\log 10+2\log 3-\log 2=\log 45$

Step-by-step explanation:

Given : Expression $\log 10+2\log 3-\log 2$

To find : Express the expression in one logarithm ?

Solution :

Using logarithmic properties,

$a\log x=\log x^a$

$\log ab=\log a+\log b$

$\log \frac{a}{b}=\log a-\log b$

$\log 10+2\log 3-\log 2=\log 10+\log 3^2-\log 2$

$\log 10+2\log 3-\log 2=\log 10+\log 9-\log 2$

$\log 10+2\log 3-\log 2=\log (\frac{10\times 9}{2})$

$\log 10+2\log 3-\log 2=\log 45$

Therefore, $\log 10+2\log 3-\log 2=\log 45$

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