Natural logarithm or common logarithm question?

[super_chris1234]

Hi,

When given an exponnential function such as 7^2x+5=2^3+7x, would I solve it using natural logarithms or common logarithms?

THis is the work I've done so far:
log(7^2x+5)=log(2^7x+3)

(2x+5)(log7)=(7x+3)(log2)

2xlog5+5log7=7xlog2+3log2

2xlog5-7xlog2=-5log7+3log2

x(2log-7log2)=-5log7+3log2

x=-5log7+3log2/2log7-7log2

x=4.68

Any help on how to solve would be greatly appreciated.

Thank you all so very much

 

[pappus]

Hi,

When given an exponnential function such as 7^2x+5=2^3+7x, would I solve it using natural logarithms or common logarithms?

THis is the work I've done so far:
log(7^2x+5)=log(2^7x+3)

(2x+5)(log7)=(7x+3)(log2)

2xlog5+5log7=7xlog2+3log2

2xlog5-7xlog2=-5log7+3log2

x(2log-7log2)=-5log7+3log2

x=-5log7+3log2/2log7-7log2

x=4.68

Any help on how to solve would be greatly appreciated.

Thank you all so very much

It doesn't matter which kind of logarithms you use:

\(\displaystyle 7^{2x+5}=2^{3+7x}\)

\(\displaystyle 7^5 \cdot (7^2)^x=2^3 \cdot (2^7)^x\)

\(\displaystyle \displaystyle{\frac{(7^2)^x}{(2^7)^x}=\frac{2^3}{7^5}}\)

\(\displaystyle \displaystyle{\left(\frac{(7^2)}{(2^7)}\right)^x= \frac{2^3}{7^5}}\)

Now you have to use logarithms (I'll take natural logs):
\(\displaystyle \displaystyle{x = \frac{\ln \left( \frac{2^3}{7^5} \right)}{\ln \left( \frac{7^2}{2^7} \right) } \approx 7.967}\)

 

[lookagain]

Hi,

When given an exponnential function such as 7^2x+5=2^3+7x,
You must use grouping symbols, such as this, else it's wrong:
7^(2x + 5) = 2^(3 + 7x)


would I solve it using natural logarithms or common logarithms?

THis is the work I've done so far:

log(7^2x+5)=log(2^7x+3) log[7^(2x + 5)] = log[2^(7x + 3)]


(2x+5)(log7)=(7x+3)(log2)

2xlog5+5log7=7xlog2+3log2

2xlog5-7xlog2=-5log7+3log2

x(>2log<-7log2)=-5log7+3log2 It is missing a "5" - - - It must be "2log5."

x=-5log7+3log2/2log7-7log2
Again, you must use grouping symbols.
x = (-5log7 + 3log2)/(2log7 - 7log2)

Also, for better readability, you should use more spacing in between
characters and/or expressions as I have shown.

 

[masters]

Hi,

When given an exponnential function such as 7^2x+5=2^3+7x, would I solve it using natural logarithms or common logarithms?

THis is the work I've done so far:
log(7^2x+5)=log(2^7x+3)

(2x+5)(log7)=(7x+3)(log2)

2xlog5+5log7=7xlog2+3log2

2xlog5-7xlog2=-5log7+3log2

x(2log-7log2)=-5log7+3log2

x=-5log7+3log2/2log7-7log2

x=4.68 <=================== INCORRECT

Any help on how to solve would be greatly appreciated.

Thank you all so very much

Hi super_chris1234,

You did good right up to the very end.

\(\displaystyle \displaystyle{x=\frac{3 \log 2 - 5 \log 7}{2 \log 7 - 7 \log 2}}\)

\(\displaystyle \displaystyle{x \approx 7.967}\)