Question

find 'x' if 2log5+1/2 log 9- log 3 = log x
​

Answer 1

→ Answer :

x = 25

→ Formulas :

  $\rightarrow m\log n=\log m^n$

  $\rightarrow\log x=\log m\\\\ \rightarrow x=m$

→ Step-by-step explanation :

$2\log5+\frac{1}{2} \log9-\log3=\log x\\\\=>\log5^2+\log9^{\frac{1}{2}}-\log3=logx\\\\=>\log25+log3-log3=logx\\\\=>\log25=\log x\\\\=>x=25$

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Answer 2

Answer:

The given equation is

2\log 5+\frac{1}{2}\log 9-\log 3 =\log x2log5+

2

1

log9−log3=logx

We need to find the value of x.

Using power property of logarithm, the given equation can be rewritten as

\log 5^2+\log 9^{\frac{1}{2}}-\log 3 =\log xlog5

2

+log9

2

1

−log3=logx [\because \log_a x^n=n\log_a x][∵log

a

x

n

=nlog

a

x]

\log 25+\log 3-\log 3 =\log xlog25+log3−log3=logx

\log 25 =\log xlog25=logx

On comparing both sides we get

x=25