Question

Write the exponential form of log7 1/343=-a​

Answer 1

The given expression:

$\log _7 \dfrac{1}{343}$ = - a

We have to write the exponential form of the given expression.

Solution:

∴ $\log _7 \dfrac{1}{343}$ = - a

∵ 347 = 7 × 7 × 7 = $7^{3}$

$\log _7 \dfrac{1}{7^3}$ = - a

Using the logarithm identity:

$\log \dfrac{1}{m^n}=\log m^{-n}$

⇒ $\log _7 7^{-3}$ = - a

⇒ - $\log _7 7^{3}$ = - a

⇒ $\log _7 7^{3}$ = a

⇒ $7^{a}$ = $7^{3}$ [ ∵ Using the logarithm property]

⇒ $\dfrac{7^{a}}{7^{3}}$ = 1

⇒ $7^{a-3}$ = 1

⇒ $7^{a-3}$ - 1 = 0

∴ The exponential form of $\log _7 \dfrac{1}{343}$ = - a is $7^{a-3}$ - 1 = 0 or, $7^{a}$ = $7^{3}$ .