What is 2log_{x}(8)+5log_{x}(z-4) ?

The solution to 2log_{x}(8)+5log_{x}(z-4) is log_{x}(64(z-4)^5)

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simplify 2log_{x}(8)+5log_{x}(z-4)

simplify

2 lo g_{x} (8) + 5 lo g_{x} (z - 4)

lo g_{x} (64 (z - 4)^{5})

Solution steps

2 lo g_{x} (8) + 5 lo g_{x} (z - 4)

Apply log rule:

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

2 lo g_{x} (8) = lo g_{x} (8^{2})

= lo g_{x} (8^{2}) + 5 lo g_{x} (z - 4)

Apply log rule:

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

5 lo g_{x} (z - 4) = lo g_{x} ((z - 4)^{5})

= lo g_{x} (8^{2}) + lo g_{x} ((z - 4)^{5})

Apply log rule:

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

lo g_{x} (8^{2}) + lo g_{x} ((z - 4)^{5}) = lo g_{x} (8^{2} (z - 4)^{5})

= lo g_{x} (8^{2} (z - 4)^{5})

8^{2} = 64

= lo g_{x} (64 (z - 4)^{5})

lo g_{e} (\frac{16}{21})

ln (\frac{e ^{5}}{7})

ln (65000) - ln (61000)

ln (336 \cdot 1 0^{4})

\frac{ln ( 4 )}{ln ( 4 ) - 2 ln ( 3 )}

What is 2log_{x}(8)+5log_{x}(z-4) ?
The solution to 2log_{x}(8)+5log_{x}(z-4) is log_{x}(64(z-4)^5)