Condense into a single logarithmic equation: log₇(x²) + log₇x - ((5log₇x)/2)

Answer 1

((5log₇x)/2) is the same as (5/2)log₇(x) which is the same as log₇(x^5/2)

Adding logs is the same as multiplying the arguments (i.e., log(m) + log(n) = log(m•n) so:

log₇(x²) + log₇(x) = log₇(x²•x) = log₇(x³)

Subtracting logs is the same as dividing the arguments (i.e., log(m) - log(n) = log(m/n) so:

log₇(x³) - log₇(x^5/2) = log₇(x³/x^5/2)

Dividing numbers with the base means subtracting their exponents so:

log₇(x³/x^5/2) = log₇(x^3-5/2) = log₇(x^6/2-5/2) = log₇(x^1/2)

Answer 2

Condense into a single logarithmic equation: log₇(x²) + log₇x - ((5log₇x)/2)

Simplify 1st quantity by using power rule

log₇x²=2 log₇x

2log₇x+log₇x-5/2*log₇x

3log₇x-5/2log₇x

if I simplify further

6/2log₇x-5/2log₇x

1/2log₇x is the answer

Answer 3

See the videa.

Answer 4

log₇(x²)+log₇(x)-5log₇(x)/2 = log₇(x²x)-log₇(x^5/2) = log₇(x³/x^5/2) = log₇(x^1/2)