Question

log x = log 125/log1/5
solve for x​

Answer 1

x = 1/1000

Given:

$logx = \frac{log125}{log\frac{1}{5} }$

To Find:

x =?

Solution:

$logx = \frac{log125}{log\frac{1}{5} }$

(log₁₀a - log₁₀b = log₁₀$\frac{a}{b}$)

$logx = \frac{log5^3}{log1 - log5}$

(log1 = 0 and logaⁿ = nloga)

$logx = \frac{3log5}{0 - log5}$

$logx = \frac{3log5}{-log5}$

logx = -3

If the base is not mentioned, then the base is 10.

log₁₀x = -3

(logₐN = x ⇔ N = aˣ)

x = 10⁻³

x = 1/10³

x = 1/1000

x = 1/1000

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