What is log_{10}(10^{log_{2}(3x)}) ?

The solution to log_{10}(10^{log_{2}(3x)}) is log_{2}(3)+log_{2}(x)

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simplify log_{10}(10^{log_{2}(3x)})

simplify

lo g_{10} (1 0^{l o g_{2} (3 x)})

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

Solution steps

lo g_{10} (1 0^{l o g_{2} (3 x)})

Apply log rule:

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

= lo g_{2} (3 x)

Apply log rule:

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

lo g_{2} (3 x) = lo g_{2} (3) + lo g_{2} (x)

= lo g_{2} (3) + lo g_{2} (x)

2 (4) + 1

∣ 2 + 3 ∣

8 x^{3} + 4 x^{2} - 4 x

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

2 (q - 6 r + 10)

What is log_{10}(10^{log_{2}(3x)}) ?
The solution to log_{10}(10^{log_{2}(3x)}) is log_{2}(3)+log_{2}(x)