Question

If log5 (x² + x) – log5 (x + 1) = 2, then the value of x is. ​

Answer 1

Hello, Buddy!!

ɢɪᴠᴇɴ:

• $\bold{log_{5}(x²+x) - log_{5}(x+1) = 2}$

ᴛᴏ ꜰɪɴᴅ:

• Value of x.

ʀᴇQᴜɪʀᴇᴅ ꜱᴏʟᴜᴛɪᴏɴ:

$\mapsto\;{\bold{log_{5}(x²+x)-log_{5}(x+1) = 2}}$

$\mapsto\;{\bold{log_{5}x(x+1)-log_{5}(x+1) = 2}}$

$\mapsto\;{\bold{log_{5}\frac{x\cancel{(x+1)}}{\cancel{(x+1)}}}}$

$\mapsto\;{\bold{log_{5}x = 2}}$

$\mapsto\;{\bold{x = {5}^{2}}}$

$\mapsto\;{\bold{x = 25}}$

• Value of x ☞ 25.

✯ logM-logN = log(M/N)

$\boxed{\tt{@MrMonarque}}$

Hope It Helps You ✌️

Answer 2

Answer:

The value of x would be 25.

Step-by-step explanation:

Given,

log_5(x^2 + x) - log_5 (x+1) = 2log5(x2+x)−log5(x+1)=2

log_5(\frac{x^2+x}{x+1})=2log5(x+1x2+x)=2 (\because log a - log b = log(\frac{a}{b}))(∵loga−logb=log(ba))

log_5(\frac{x(x+1)}{x+1})=2log5(x+1x(x+1))=2

log_5x = 2log5x=2

\implies x = 5^2=25⟹x=52=25 (log_a x = b\implies x = a^b)(logax=b⟹x=ab)

Hence, the value of x would be 25.