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Popular >

simplify log_{49}(sqrt(7))

Solution

simplify

lo g_{49} (7)

Solution

\frac{1}{4}

+1

Decimal Notation

0.25

Solution steps

lo g_{49} (7)

Factor the number:

49 = 7^{2}

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

Apply log rule:

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

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

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

Apply radical rule:

a = a^{\frac{1}{2}}

7 = 7^{\frac{1}{2}}

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

Apply log rule:

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

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

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

\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}

= \frac{1}{4}

Popular Examples

| n/4 |<= 3\mid

\frac{n}{4} \leq 3 ∣

simplify sqrt(100/4)simplify

\frac{100}{4}

factor k^2-13k+22 factor

k^{2} - 13 k + 22

∣ x - 5 ∣ \geq 3

simplify-1/2*3/4 simplify

- \frac{1}{2} \cdot \frac{3}{4}

Frequently Asked Questions (FAQ)

What is log_{49}(sqrt(7)) ?
The solution to log_{49}(sqrt(7)) is 1/4