Use Logarithms to solve the equation 7^x = 2^(x+1) giving the value of x to 3sf

currently doing core 2 mathematics and am stuck on this one. any help would be appreciated

Question

Use Logarithms to solve the equation 7^x = 2^(x+1) giving the value of x to 3sf

currently doing core 2 mathematics and am stuck on this one. any help would be appreciated

anonymous · Answer

$$7^x=2^{x+1}$$

anonymous · Answer

alright, where are you stuck at? The general application of logarithmns? Or does it confuse you because you have unlike bases?

anonymous · Answer

7^x = 2^(x+1)

I take logs of both sides ending up with

xln7=(x+1)ln2

where to go from here?

anonymous · Answer

very good so far, distribute the right hand side, regular distribution property and then save the linear equation for x.

anonymous · Answer

so is that

xln7 = xln2 + ln2

anonymous · Answer

exactly, now try to solve for x, getting it on the same side and factor it out (distribution property in reverse -> factorisation)

anonymous · Answer

xln7 - xln 2 = ln2

x(ln7-ln2) = ln2
x(ln3.5) = ln2
x=ln2 over ln3.5

anonymous · Answer

there you go.

anonymous · Answer

xln7 = xln2 + ln2 is what i was struggling with. thankyou for your help

anonymous · Answer

you're very welcome!