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Number - Solving Indices with Algebra Questions

  a - answer    s - solution    v - video

Question 1


Find the value of $x$:

a) $3^x=9$  a s v
b) $4^x=64$  a s v
c) $2^x=32$  a s v
d) $8^x=8$  a s v
e) $12^x=144$  a s v
f) $5^x=1$  a s v
g) $(-3)^x=-27$  a s v
h) $\left(\frac12\right)^x=\frac{1}{16}$  a s v


Question 2


Find the value of $x$:

a) $5^x=\frac15$  a s v
b) $10^x=\frac{1}{100}$  a s v
c) $\left(\frac12\right)^x=2$  a s v
d) $\left(\frac13\right)^x=9$  a s v
e) $\left(\frac23\right)^x=\frac{8}{27}$  a s v
f) $\left(\frac45\right)^x=\frac{25}{16}$  a s v


Question 3


Find the value of $x$:

a) $16^x=4$  a s v
b) $81^x=9$  a s v
c) $125^x=5$  a s v
d) $\left(\frac{9}{49}\right)^x=\frac37$  a s v
e) $\left(\frac{100}{81}\right)^x=\frac{9}{10}$  a s v
f) $\left(\frac{4}{9}\right)^x=\frac{8}{27}$  a s v
g) $\left(\frac{27}{8}\right)^x=\frac{4}{9}$  a s v
h) $\left(4\right)^x=\frac{1}{32}$  a s v


Question 4


Find the value of $x$:

a) $2^{2x+1}=32$  a s v
b) $9^{1-2x}=81$  a s v
c) $8^{4x}=16$  a s v
d) $11^{\frac x3}=\frac{1}{121}$  a s v
e) $4^x\times4^x=64$  a s v
f) $5^{3x}\div5^x=625$  a s v
g) $3^{6x}\times3^{3x}=\frac19$  a s v
h) $25^{7x}\times25^{6x}\div25^{x}=125$  a s v


Question 5


Find the value of $x$:

a) $5^x\times25^x=125$  a s v
b) $2^x\times8^x=2$  a s v
c) $10^{2x}\times1000^x=100$  a s v
d) $9^{x+1}\times3^{2x}=\sqrt3$  a s v


Question 6


Find the value of $x$:

a) $3\times3^x=9$  a s v
b) $5\times5^{x+1}=5$  a s v
c) $36\times6^x=\frac16$  a s v
d) $8\div2^{3x+2}=2$  a s v


Question 7


Find the value of $x$:

a) $3^x+3^x+3^x=81$  a s v
b) $2^x+2^x=\frac14$  a s v
c) $4^x+4^x+4^x+4^x=2$  a s v
d) $3^{2x+3}+3^{2x+3}+3^{2x+3}=9^5$  a s v