Question

How would I go about solving for x in this equation?

49^x = 7^(x – 3)

Answer 1

\[49^{x}=7^{x-3}\]

Answer 2

Hint*

\[\large a^x = x \times \ln a\]

So take the log of both sides here...

\[\large \ln 49^x = \ln 7^{x - 3}\]

becomes

\[\large x \times \ln 49 = (x-3) \times \ln 7 \]

Can you take it from there?

Answer 3

yes thank you so much!!!:)

Answer 4

Anytime :)

Answer 5

@cayssaday do you understand it ? but this is possible solving without logarithm natural

so

in the left side there is 49 on exponent x ,yes ?
but you know that 49 is equal 7 squared

so in this case in the left side will be 7^(2x)
and on the right side there is 7^(x-3)

so than now you see that there is 7 on exponent 2x equal 7 on exponent (x-3)

so you know that than the numbers ,like in this case 7 ,with one exponent are the same so than the left side will be equal right side than the exponents are equales

so make equale 2x=x-3

solve it for x and will get the right value for x

hope this is understandably sure right easy

Answer 6

@jhonyy9 Thank yous so much, your explanation was awesome and helped a lot!!:)

Answer 7

was my pleasure

good luck