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Popular >

simplify log_{25}(49)

Solution

simplify

lo g_{25} (49)

Solution

lo g_{5} (7)

+1

Decimal Notation

1.20906 \dots

Solution steps

lo g_{25} (49)

Factor the number:

49 = 7^{2}

= lo g_{25} (7^{2})

Apply log rule:

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

lo g_{25} (7^{2}) = 2 lo g_{25} (7)

= 2 lo g_{25} (7)

Factor the number:

25 = 5^{2}

= 2 lo g_{5^{2}} (7)

Apply log rule:

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

lo g_{5^{2}} (7) = \frac{1}{2} lo g_{5} (7)

= 2 \cdot \frac{1}{2} lo g_{5} (7)

2 \cdot \frac{1}{2} lo g_{5} (7) = lo g_{5} (7)

= lo g_{5} (7)

Popular Examples

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\frac{( 2 x - 3 )}{6} - 2 (\frac{3}{2} x - 1) - \frac{3 - 2 x}{3} = 0

factor-45x^8y^2z^4-18x^4y^6z^7 factor

- 45 x^{8} y^{2} z^{4} - 18 x^{4} y^{6} z^{7}

3 x + 1 = 8 x - 24

m + 14 = 81

simplify (2*5)/2 simplify

\frac{2 \cdot 5}{2}

Frequently Asked Questions (FAQ)

What is log_{25}(49) ?
The solution to log_{25}(49) is log_{5}(7)