Question

log5(x+5) = 1 then ‘x’ = . . . .

a) 1 b) 0 c) 5 d) -5​

Answer 1

Given,

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

Base change formula

$\sf \: log_{a}(b) = \dfrac{ log(b) }{ log(a) }$

Thus,

$\longrightarrow \sf \dfrac{log_{}(x + 5) }{log(5)} = 1 \\ \\ \longrightarrow \sf log(x + 5) = log(5) \\ \\ \longrightarrow \sf \: x + 5 = 5 \\ \\ \longrightarrow \sf \: x = 0$

Option (b) is correct.

Answer 2

♣ Qᴜᴇꜱᴛɪᴏɴ :

$\sf{Find\:the\:value\:of\:x\:in\::\:\large\boxed{\sf{log_5\left(x+5\right)=1}}}$

★═════════════════★

♣ ᴀɴꜱᴡᴇʀ :

$\huge\boxed{\sf{x=0}}$

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♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ :

$\large\boxed{\sf{\log _5\left(x+5\right)=1}}$

Use the logarithmic definition: If  $\sf{ \log _{a}(b)=c \text { then } b=a^{c}}$

$\log _5\left(x+5\right)=1\quad \Rightarrow \quad \:x+5=5^1$

$x+5=5^1$

$x+5=5$

Solve $x+5=5$

$\mathrm{Subtract\:}5\mathrm{\:from\:both\:sides}$

$x+5-5=5-5$

$\huge\boxed{\sf{x=0}}$