What is log_{10}(30^{7log_{10}(1)}) ?

The solution to log_{10}(30^{7log_{10}(1)}) is 0

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simplify log_{10}(30^{7log_{10}(1)})

simplify

lo g_{10} (3 0^{7 l o g_{10} (1)})

0

Solution steps

lo g_{10} (3 0^{7 l o g_{10} (1)})

7 lo g_{10} (1) = 0

= lo g_{10} (3 0^{0})

Apply log rule:

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

lo g_{10} (3 0^{0}) = 7 lo g_{10} (1) lo g_{10} (30)

= 7 lo g_{10} (1) lo g_{10} (30)

lo g_{10} (1) = 0

lo g_{10} (30) = 1 + lo g_{10} (3)

= 7 \cdot 0 \cdot (1 + lo g_{10} (3))

Apply rule:

a \cdot 0 = 0

= 0

\frac{\frac{3}{2}}{4}

(3 x + 2) (x + 3)

(2 x - 2 y)^{3}

\frac{h}{h}

e^{l n (x) + l n (3)}

What is log_{10}(30^{7log_{10}(1)}) ?
The solution to log_{10}(30^{7log_{10}(1)}) is 0