Question

Log subscript 7(8x+20)=Log subscript 7(x+6) . Solve for x

Answer 1

If\[\Large \log_{7}(8x+20)=\log_{7}(x+6)\]then\[\Large 8x+20=x+6\]

Answer 2

Use the property of logarithms that \(b^{\log_b{a}} = a\)

Answer 3

So now how do you solve ?

Answer 4

Do you know how to solve
8x + 20 = x + 6 ?

Answer 5

got x=-2

Answer 6

That's your answer

Answer 7

That's correct!

Answer 8

log subscript4(4x) + log subscript 4(x)= Log subscript 4(64)

Answer 9

solve for x

Answer 10

\[\log{a}+\log{b} = \log{(a*b)}\]

Answer 11

So you can rewrite as \(\log_4{(4x*x)} = \log_4(64)\) or \(\log_4{(4x^2)} = \log_4(64)\) From there you should be able to solve as in the previous problem.

Answer 12

x=4

Answer 13

Let's check:

\[\log_4{4(4)} + \log_4{4} = \log_4{64}\]\[\log_4 16 + \log_4 4 = \log_4 64\]\[2+1=3\checkmark\]