Question

Solve 3^x – 4 = 7^x + 9

Answer 1

x ≈ –25.86

x ≈ –2.59

x ≈ –0.39

x ≈ –0.04

Answer 2

if this is
\[ 3^{x-4}= 7^{x+9} \]
can you take the log of both sides ?

Answer 3

How would i go about doing that?

Answer 4

you write log next to each term

Answer 5

Like log3^x-4 = log7^x+9?

Answer 6

yes, but put in parens
log (3^(x-4) ) = log(7^(x+9) )
which looks nicer if you use the equation editor (see button on the bottom left of where you type in)
\[ \log\left(3^{x-4}\right) = \log\left(7^{x+9}\right) \]

Answer 7

now use this property
\[ \log(a^b) = b\log(a) \]
to rewrite both sides.

Answer 8

What is a & b?

Answer 9

you do pattern matching. match the rule to your expression.

Answer 10

log(3^x4) = ()7log(x+9)?

Answer 11

Here is an example of how to interpret the rule
\[ \log(a^b) = b\log(a) \]
if you have the problem
\[ \log(y^3) \]
you match the y to the a (both are the "base")
and match 3 to the b (both are "exponents")
once you figure out that the 3 matches the b, you use the 2nd part
\[ b\log(a) \]
to re-write it as
\[ 3 \log(y) \]

Answer 12

in your case, what matches to the a ?
what matches the b? (what is the exponent)

Answer 13

use the rule on the left side of
\[ \log\left(3^{x-4}\right) = \log\left(7^{x+9}\right) \]

can you match
\[ \log\left(3^{x-4}\right) \text{ to } \log(a^b) \]

Answer 14

what matches to the a ?
what matches the b? (what is the exponent)