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Margaret [11]
3 years ago
15

Solve the exponential equation. (logs) 3(1.05)^x+1=6

Mathematics
1 answer:
Arte-miy333 [17]3 years ago
8 0
\bf 3(1.05)^x+1=6\implies 3(1.05)^x=5\implies (1.05)^x=\cfrac{5}{3}\\\\
-----------------------------\\\\
log_{{  a}}\left( x^{{  b}} \right)\implies {{  b}}\cdot  log_{{  a}}(x)\qquad thus\\\\
-----------------------------\\\\
log\left[  (1.05)^x \right]=log\left( \cfrac{5}{3} \right)\implies xlog\left[  (1.05) \right]=log\left( \cfrac{5}{3} \right)
\\\\\\
x=\cfrac{log\left( \frac{5}{3} \right)}{log(1.05)}
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