Question

HELP!
log(base 25) (6x+25) +log (base 5) (x+25)=5

Answer 1

\[ \log_{25} (6x+25) +\log_{5} (x+25)=5\]

Answer 2

The sum of logs is the log of the product.
log(a) + log(b) = log(ab)
Do that to the left side

Answer 3

I just noticed, are the logs on the left side different bases, 5 and 25?

Answer 4

I changed the base and got \[\log_{5} (6x+25)(x+25)^{2} =\log_{5} 5 ^{10}\]

Answer 5

log(base5)(x + 25) = log(base 5)(x + 25). It's already base 5
log(base 25)(6x + 25) = log(base5)?

Answer 6

I think the change of base is incorrect...

\[\log_{25}(6x +25) = \frac{\log_{5}(6x + 5)}{\log_{5}(25)} = \frac{1}{2} \log_{5}(6x + 5)\]

Answer 7

log(base25)(6x + 25) = (log(base5)(6x + 25))/log(base5)(25)

Answer 8

log25(6x + 25) = log5( (1/2)(6x + 25) )

Answer 9

thats wrong...

\[\log_{5}(25) = \log_{5}(5^2) = 2\]

so the 1/2 is outside the log...

\[\frac{1}{2} \log_{5}(6x + 5) = \log_{5}(6x + 5)^{\frac{1}{2}}\]

Answer 10

@campbell_st Right, my mistake.
log25(6x + 25) = (1/2)log5(6x + 25)

Answer 11

but what will I do with the \[\log_{5} (x+25)=\log_{5} 5^{5} ?? \] after the equation you gave?

Answer 12

That you have the same base on the left side for both logs, you can combine them: