What is log_{10}(64)+1/2 log_{10}(7)-log_{10}(8) ?

The solution to log_{10}(64)+1/2 log_{10}(7)-log_{10}(8) is log_{10}(8sqrt(7))

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simplify log_{10}(64)+1/2 log_{10}(7)-log_{10}(8)

simplify

lo g_{10} (64) + \frac{1}{2} lo g_{10} (7) - lo g_{10} (8)

lo g_{10} (87)

Decimal Notation

1.32563 \dots

Solution steps

lo g_{10} (64) + \frac{1}{2} lo g_{10} (7) - lo g_{10} (8)

Apply log rule:

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

\frac{1}{2} lo g_{10} (7) = lo g_{10} (7^{\frac{1}{2}})

= lo g_{10} (64) + lo g_{10} (7^{\frac{1}{2}}) - lo g_{10} (8)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (64) + lo g_{10} (7^{\frac{1}{2}}) = lo g_{10} (64 \cdot 7^{\frac{1}{2}})

= lo g_{10} (64 \cdot 7^{\frac{1}{2}}) - lo g_{10} (8)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (64 \cdot 7^{\frac{1}{2}}) - lo g_{10} (8) = lo g_{10} (\frac{64 \cdot 7 ^{\frac{1}{2}}}{8})

= lo g_{10} (\frac{64 \cdot 7 ^{\frac{1}{2}}}{8})

Divide the numbers:

\frac{64}{8} = 8

= lo g_{10} (8 \cdot 7^{\frac{1}{2}})

Apply exponent rule:

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

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

= lo g_{10} (87)

lo g_{10} (\frac{3 x}{yz})

1 + lo g_{10} (2 x)

lo g_{5} (12) - lo g_{5} (6)

3 lo g_{2} (x) - (lo g_{2} (3) - lo g_{2} (x + 4))

lo g_{3} (x + 1) - lo g_{3} (x^{2} - 1)

What is log_{10}(64)+1/2 log_{10}(7)-log_{10}(8) ?
The solution to log_{10}(64)+1/2 log_{10}(7)-log_{10}(8) is log_{10}(8sqrt(7))