What is expand log_{10}(4(x+8)^5) ?

The solution to expand log_{10}(4(x+8)^5) is 2log_{10}(2)+5log_{10}(x+8)

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expand log_{10}(4(x+8)^5)

expand

lo g_{10} (4 (x + 8)^{5})

2 lo g_{10} (2) + 5 lo g_{10} (x + 8)

Solution steps

lo g_{10} (4 (x + 8)^{5})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{10} (4 (x + 8)^{5}) = lo g_{10} (4) + lo g_{10} ((x + 8)^{5})

= lo g_{10} (4) + lo g_{10} ((x + 8)^{5})

Apply log rule:

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

lo g_{10} ((x + 8)^{5}) = 5 lo g_{10} (x + 8)

= lo g_{10} (4) + 5 lo g_{10} (x + 8)

lo g_{10} (4) = 2 lo g_{10} (2)

= 2 lo g_{10} (2) + 5 lo g_{10} (x + 8)

lo g_{10} (4 x + 3) - lo g_{10} (x)

lo g_{2} (x z^{3})

lo g_{\frac{1}{2}} (16 z (x^{3} - 27))

ln (\frac{e ^{x} + e ^{- x}}{2})

ln (z) - ln (a + 15) + ln (z - 5)

What is expand log_{10}(4(x+8)^5) ?
The solution to expand log_{10}(4(x+8)^5) is 2log_{10}(2)+5log_{10}(x+8)