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Popular >

simplify log_{49}(343)

Solution

simplify

lo g_{49} (343)

Solution

\frac{3}{2}

+1

Decimal Notation

1.5

Solution steps

lo g_{49} (343)

Factor the number:

49 = 7^{2}

= lo g_{7^{2}} (343)

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{7^{2}} (343) = \frac{1}{2} lo g_{7} (343)

= \frac{1}{2} lo g_{7} (343)

Factor the number:

343 = 7^{3}

= \frac{1}{2} lo g_{7} (7^{3})

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{7} (7^{3}) = 3

= \frac{1}{2} \cdot 3

\frac{1}{2} \cdot 3 = \frac{3}{2}

= \frac{3}{2}

Popular Examples

simplify (\sqrt[3]{-5})/(40^{1/3)}simplify

\frac{1}{2} x + 3 < 4 x - 7

factor (5a-3b)^2-25a^2 factor

(5 a - 3 b)^{2} - 25 a^{2}

-2(3y-6)+4(5y-8)=92

- 2 (3 y - 6) + 4 (5 y - 8) = 92

simplify (5+sqrt(3))/(2-sqrt(3))simplify

\frac{5 + 3}{2 - 3}

Frequently Asked Questions (FAQ)

What is log_{49}(343) ?
The solution to log_{49}(343) is 3/2