Question

Log question, 10^(x+3) = 6^(2x), solve for x

Answer 1

the answer is \[\frac{ 3\ln10 }{ \ln18-\ln5 }\]

but i don't know how to get there, help please?

Answer 2

use the rule
\[ ln(x^a) = a \cdot ln(x) \]

Answer 3

yea i tried, got
\[\frac{ 2x \ln6 }{ lnl0 } - x = 3\]

but dunno how to continue..

Answer 4

(x+3) ln(10)= 2x ln(6)
is how I start out

Answer 5

yea but Im unable to get the answer exactly like that

Answer 6

continuing

(x+3) ln(10)= 2x ln(6)
rewrite 2 x ln(6) as x ln(6^2) because the final answer seems to want this
also distribute the ln(10) on the left side:

x ln(10) + 3 ln(10)= x ln(36)

they have 3 ln(10) up top, so subtract x ln(10) from both sides

Answer 7

what about x= 3/2log(6)-1

Answer 8

would that be right?

Answer 9

x ln(36)- x ln(10) = 3 ln(10)
x (ln(36)- ln(10)) = 3 ln(10)

to simplify the left side. notice that ln(36)- ln(10) = ln(36/10)= ln(18/5)= ln(18)-ln(5)

x ( ln(18)-ln(5))= 3 ln(10)

Answer 10

divide through to get their answer
x= 3 ln(10)/ ( ln(18)- ln(5))

any of the steps confusing?

Answer 11

@KE8717504 Yes, if you mean log base 10, and you put parens in like this:
3/(2 log(6)-1)

Answer 12

Yes.

Answer 13

OMFG @phi THANKS SO MUCH

Answer 14

If we pick up where you left off:
yea i tried, got
\[\frac{ 2x \ln6 }{ ln10 } - x = 3 \]
but dunno how to continue..
factor out the x on the left side. also bring the back inside the ln:

\[ (\frac{ln36}{ln(10) }-1)x= 3 \]
or
\[ (\frac{ln36}{ln10 }-\frac{ln10}{ln{10}})x= 3 \]
multiply both sides by ln10
\[(ln36-ln10)x= 3 ln10 \]
simplify the left side like before, and you get to the answer...