Question

7^x+3=5^x

Answer 1

what are you trying to do?

Answer 2

solve the exponential equation

Answer 3

First of all, this is a question based on logarithm. So have you studied how to use log ?

Answer 4

Sorry, forget my above comment.

Answer 5

Are you looking for real values of x ? @cfrazier1

Answer 6

yes

Answer 7

the answer choices are A)-17.350 B)17.350 C) -18.700 D)-16.00

Answer 8

First of all answer me this:

(1) If x would have been +ve, then which would be larger 7^x or 5^x ?

Answer 9

The question is this:

\[\large{7^x + 3 = 5^x}\]

Answer 10

Right ?

Answer 11

Yes

Answer 12

no its 7^(x+3)=5^x

Answer 13

Yeah I though so

Answer 14

Great then we are done.

Answer 15

See:
\[\large{7^{x+3} = 5^x}\]

OKay ?

Answer 16

yes

Answer 17

Good, then can you take log both sides ?

Answer 18

I would prefer taking log with base 10.

Answer 19

ok

Answer 20

Okay so we get:

\[\large{\log{7^{x+3}} = \log{5^x}}\]


Now, do you know this property:

\[\large{\log(a^b) = b\log(a)}\] ?

Answer 21

yes

Answer 22

Very good

Answer 23

So, can you apply this property here ?

Answer 24

\[\large{\log(7^{x+3}) = \log(5^x)}\]
\[\large{\implies (x+3)\log 7 = x\log 5}\]

Get this ?

Answer 25

@cfrazier1 ?