Logs, Roots And Sevens

Algebra Level 2

$\large \log_7 \log_7 \sqrt{7\sqrt{7\sqrt 7}} = \, ?$

0

1

3\log_2 7

3\log_7 2

1- 3\log_2 7

1- 3\log_7 2

Cannot be determined

1 solution

Chew-Seong Cheong
Jun 29, 2016

Relevant wiki: Properties of Logarithms - Basic

$\begin{aligned} \log_7 \log_7 \sqrt{7\sqrt{7\sqrt 7}} & = \log_7 \log_7 \left( 7 \left(7 \left(7\right)^\frac 12 \right)^\frac 12 \right)^\frac 12 = \log_7 \log_7 \left( 7 \left(7^\frac 32 \right)^\frac 12 \right)^\frac 12 = \log_7 \log_7 \left( 7 \cdot 7^\frac 34 \right)^\frac 12 = \log_7 \log_7 \left(7^\frac 74 \right)^\frac 12 \\ & = \log_7 \log_7 7^\frac 78 = \log_7 \frac 78 = \log_7 7 - \log_7 8 = 1 - \log_7 2^3 = \boxed{1-3\log_7 2} \end{aligned}$

From where that 3/2 came

Vedant Sarnobat - 4 years, 7 months ago

$7\left(7^\frac 12\right) = 7^1\cdot 7^\frac 12 = 7^{1+\frac 12} = 7^\frac 32$

Chew-Seong Cheong - 4 years, 7 months ago

Law of exponent: 7^1 x 7^1/2 = 7 ^ (1+ 1/2) = 7^3/2

Brendix Emata - 4 years, 7 months ago

Logs, Roots And Sevens

1 solution

0 pending reports