Question

log 10 5+log 10(5x+1)-1=log 10(x+5)​

Answer 1

Answer:

★Question★

Solve for x :-

$\bf \: log_{10}(5) + log_{10}(5x + 1) - 1 = log_{10}(x + 5)$

★Answer★

★Given :-

$\bf \: log_{10}(5) + log_{10}(5x + 1) - 1 = log_{10}(x + 5)$

★To find :-

• Value of x

★Formula used :-

$\bf \:loga + logb = logab$

$\bf \: log_{10}(10) = 1$

★Solution:-

$\bf \: log_{10}(5) + log_{10}(5x + 1) - 1 = log_{10}(x + 5)$

$\bf \: log_{10}(5) + log_{10}(5x + 1) = log_{10}(x + 5) + 1$

$\bf \: log_{10}(5) + log_{10}(5x + 1) = log_{10}(x + 5) + log_{10}(10)$

$\bf\implies \: log_{10}(5(5x + 1)) = log_{10}(10(x + 5))$

★ On comparing, we get

$\bf\implies \:5(5x + 1) = 10(x + 5)$

$\bf\implies \:25x + 5 = 10x + 50$

$\bf\implies \:25x - 10x = 50 - 5$

$\bf\implies \:15x = 45$

$\bf\implies \:x = 3$

_____________________________________________

Answer 2

Step-by-step explanation:

★Given :-

\bf \: log_{10}(5) + log_{10}(5x + 1) - 1 = log_{10}(x + 5)log

10

(5)+log

10

(5x+1)−1=log

10

(x+5)

★To find :-

Value of x

★Formula used :-

\bf \:loga + logb = logabloga+logb=logab

\bf \: log_{10}(10) = 1log

10

(10)=1

★Solution:-

\bf \: log_{10}(5) + log_{10}(5x + 1) - 1 = log_{10}(x + 5)log

10

(5)+log

10

(5x+1)−1=log

10

(x+5)

\bf \: log_{10}(5) + log_{10}(5x + 1) = log_{10}(x + 5) + 1log

10

(5)+log

10

(5x+1)=log

10

(x+5)+1

\bf \: log_{10}(5) + log_{10}(5x + 1) = log_{10}(x + 5) + log_{10}(10)log

10

(5)+log

10

(5x+1)=log

10

(x+5)+log

10

(10)

\bf\implies \: log_{10}(5(5x + 1)) = log_{10}(10(x + 5))⟹log

10

(5(5x+1))=log

10

(10(x+5))

★ On comparing, we get

\bf\implies \:5(5x + 1) = 10(x + 5)⟹5(5x+1)=10(x+5)

\bf\implies \:25x + 5 = 10x + 50⟹25x+5=10x+50

\bf\implies \:25x - 10x = 50 - 5⟹25x−10x=50−5

\bf\implies \:15x = 45⟹15x=45

\bf\implies \:x = 3⟹x=3