Question

ALGEBRA 2 HELP:
Solve 4^(2x) = 7^(x−1).

Answer 1

be prepared to do a bunch of algebra

Answer 2

when you get back

Answer 3

From Mathematica:
\[\text{Solve}\left[\log \left(4^{2 x}\right)=\log \left(7^{x-1}\right),x\right] \]\[x=-\frac{\log (7)}{4 \log (2)-\log (7)} \]

Answer 4

Step 1: Add natural logs on both sides\[4^{2x}=7^{x-1}\]\[\log_{10}4^{2x}=\log_{10}7^{x-1}\]Step 2: Bring down the power
For example,\[=\log_{10}7^\color{red}{{8x}}\]\[=\color{red}{(8x)}\log_{10}7\]okay,now back to the question
Bring down the power\[\log_{10}4^\color{red}{(2x)}=\log_{10}7^\color{red}{(x-1)}\]\[\color{red}{(2x)}\log_{10}4=\color{red}{(x-1)}\log_{10}7\]Step 3: Divide both sides by\[\log_{10}4\]u will get\[2x=(x-1)\frac{ \log_{10}7 }{ \log_{10}4 }\]Step 4: Divide (x-1) on both sides\[\frac{ 2x }{ x-1 }=\frac{ \log_{10}7 }{ \log_{10}4 }\]Step 5: Solve it\[\frac{ 2x }{ x-1 }=1.404\]\[2x=(x-1)1.404\]\[2x=1.404x-1.404\]\[0.596x=-1.404\]\[x=\frac{ -1.404 }{ 0.596 }\]\[x=?\]solve it! @destinykiara99

Answer 5

the answer is -2.353887